PROVING THEOREM 3.2 If two parallel lines are cut by a transversal, then the pairs of

VOCABULARY Copy and complete: A line that intersects two other lines is a ? .

WRITING A table is set for dinner. Can the legs of the table and the top of the table lie in parallel planes? Explain why or why not.

IDENTIFYING RELATIONSHIPS Think of each segment in the diagram as part of a line. Which line(s) or plane(s) contain point B and appear to fit the description? G H E F D A Line(s) parallel to ] CD

IDENTIFYING RELATIONSHIPS Think of each segment in the diagram as part of a line. Which line(s) or plane(s) contain point B and appear to fit the description? G H E F D A Line(s) perpendicular to ] CD

IDENTIFYING RELATIONSHIPS Think of each segment in the diagram as part of a line. Which line(s) or plane(s) contain point B and appear to fit the description? G H E F D A Line(s) skew to ] CD

IDENTIFYING RELATIONSHIPS Think of each segment in the diagram as part of a line. Which line(s) or plane(s) contain point B and appear to fit the description? G H E F D A Plane(s) parallel to plane CDH

PARALLEL AND PERPENDICULAR LINES Use the markings in the diagram. L M K N S Name a pair of parallel lines.

PARALLEL AND PERPENDICULAR LINES Use the markings in the diagram. L M K N S Name a pair of perpendicular lines.

PARALLEL AND PERPENDICULAR LINES Use the markings in the diagram. L M K N S Is ] PN i ] KM ? Explain.

PARALLEL AND PERPENDICULAR LINES Use the markings in the diagram. L M K N S Is ] PR ] NP ? Explain.

ANGLE RELATIONSHIPS Identify all pairs of angles of the given type. 1 3 4 2 5 7 8 6 Corresponding

ANGLE RELATIONSHIPS Identify all pairs of angles of the given type. 1 3 4 2 5 7 8 6 Alternate interior

ANGLE RELATIONSHIPS Identify all pairs of angles of the given type. 1 3 4 2 5 7 8 6 Alternate exterior

ANGLE RELATIONSHIPS Identify all pairs of angles of the given type. 1 3 4 2 5 7 8 6 Consecutive interior

ERROR ANALYSIS Describe and correct the error in saying that 1 and 8 are corresponding angles in the diagram for Exercises 1114.

APPLYING POSTULATES How many lines can be drawn that fit each description? Copy the diagram and sketch all the lines. Lines through B and parallel to ] AC C B

APPLYING POSTULATES How many lines can be drawn that fit each description? Copy the diagram and sketch all the lines. Lines through A and perpendicular to ] BC C B

USING A DIAGRAM Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. 1 3 4 2 5 7 8 6 9 11 12 10 13 15 16 14 5 and 1

USING A DIAGRAM Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. 1 3 4 2 5 7 8 6 9 11 12 10 13 15 16 14 11 and 13

USING A DIAGRAM Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. 1 3 4 2 5 7 8 6 9 11 12 10 13 15 16 14 6 and 13

USING A DIAGRAM Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. 1 3 4 2 5 7 8 6 9 11 12 10 13 15 16 14 10 and 15

USING A DIAGRAM Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. 1 3 4 2 5 7 8 6 9 11 12 10 13 15 16 14 2 and 11

USING A DIAGRAM Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. 1 3 4 2 5 7 8 6 9 11 12 10 13 15 16 14 8 and 4

ANALYZING STATEMENTS Copy and complete the statement with sometimes, always, or never. Sketch examples to justify your answer. If two lines are parallel, then they are ? coplanar.

ANALYZING STATEMENTS Copy and complete the statement with sometimes, always, or never. Sketch examples to justify your answer. If two lines are not coplanar, then they ? intersect.

ANALYZING STATEMENTS Copy and complete the statement with sometimes, always, or never. Sketch examples to justify your answer. If three lines intersect at one point, then they are ? coplanar.

ANALYZING STATEMENTS Copy and complete the statement with sometimes, always, or never. Sketch examples to justify your answer. If two lines are skew to a third line, then they are ? skew to each other.

MULTIPLE CHOICE RPQ and PRS are what type of angle pair? A Corresponding B Alternate interior C Alternate exterior D Consecutive interior P P S

ANGLE RELATIONSHIPS Copy and complete the statement. List all possible correct answers. B D F J H E BCG and ? are corresponding angles.

ANGLE RELATIONSHIPS Copy and complete the statement. List all possible correct answers. B D F J H E BCG and ? are consecutive interior angles.

ANGLE RELATIONSHIPS Copy and complete the statement. List all possible correct answers. B D F J H E FCJ and ? are alternate interior angles.

ANGLE RELATIONSHIPS Copy and complete the statement. List all possible correct answers. B D F J H E FCA and ? are alternate exterior angles.

CHALLENGE Copy the diagram at the right and extend the lines. a. Measure 1 and 2. b. Measure 3 and 4. c. Make a conjecture about alternate exterior angles formed when parallel lines are cut by transversals. 1 3 4 2

CONSTRUCTION Use the picture of the cherry-picker for Exercises 34 and 35. Is the platform perpendicular, parallel, or skew to the ground?

CONSTRUCTION Use the picture of the cherry-picker for Exercises 34 and 35. Is the arm perpendicular, parallel, or skew to a telephone pole?

OPEN-ENDED MATH Describe two lines in your classroom that are parallel, and two lines that are skew.

MULTIPLE CHOICE What is the best description of the horizontal bars in the photo? A Parallel B Perpendicular C Skew D Intersecting

CONSTRUCTION Use these steps to construct a line through a given point P that is parallel to a given line m. P m P R S P T STEP 1 Draw points Q and R on m. Draw ] PQ. Draw an arc with the compass point at Q so it crosses ] QP and ] QR. STEP 2 Copy PQR on ] QP. Be sure the two angles are corresponding. Label the new angle TPS. Draw ] PS. ] PS i ] QR.

SHORT RESPONSE Two lines are cut by a transversal. Suppose the measure of a pair of alternate interior angles is 908. Explain why the measure of all four interior angles must be 908.

TREE HOUSE In Exercises 4042, use the photo to decide whether the statement is true or false. D C A B The plane containing the floor of the tree house is parallel to the ground.

TREE HOUSE In Exercises 4042, use the photo to decide whether the statement is true or false. D C A B All of the lines containing the railings of the staircase, such as ] AB , are skew to the ground.

TREE HOUSE In Exercises 4042, use the photo to decide whether the statement is true or false. D C A B All of the lines containing the balusters, such as ] CD , are perpendicular to the plane containing the floor of the tree house.

CHALLENGE Draw the figure described. Lines l and m are skew, lines l and n are skew, and lines m and n are parallel.

CHALLENGE Draw the figure described. Line l is parallel to plane A, plane A is parallel to plane B, and line l is not parallel to plane B.

Use the Law of Detachment to make a valid conclusion. (p. 87) If the measure of an angle is less than 908, then the angle is acute. The measure of A is 468.

Use the Law of Detachment to make a valid conclusion. (p. 87) If a food has less than 140 milligrams of sodium per serving, then it is low sodium. A serving of soup has 90 milligrams of sodium per serving.

Find the measure of each numbered angle. (p. 124) 1 3 2 1

Find the measure of each numbered angle. (p. 124) 1108 1 3 2

VOCABULARY Draw a pair of parallel lines and a transversal. Label a pair of corresponding angles.

WRITING Two parallel lines are cut by a transversal. Which pairs of angles are congruent? Which pairs of angles are supplementary?

MULTIPLE CHOICE In the figure at the right, which angle has the same measure as 1? A 2 B 3 C 4 D 5 1 3 2 5

USING PARALLEL LINES Find the angle measure. Tell which postulate or theorem you use. 3 5 6 7 8 2 4 If m 4 5 658, then m 1 5 ? .

USING PARALLEL LINES Find the angle measure. Tell which postulate or theorem you use. 3 5 6 7 8 2 4 If m 7 5 1108, then m 2 5 ? .

USING PARALLEL LINES Find the angle measure. Tell which postulate or theorem you use. 3 5 6 7 8 2 4 If m 5 5 718, then m 4 5 ? .

USING PARALLEL LINES Find the angle measure. Tell which postulate or theorem you use. 3 5 6 7 8 2 4 If m 3 5 1178, then m 5 5 ? .

USING PARALLEL LINES Find the angle measure. Tell which postulate or theorem you use. 3 5 6 7 8 2 4 If m 8 5 548, then m 1 5 ? .

USING POSTULATES AND THEOREMS What postulate or theorem justifies the statement about the diagram? 1 4 2 7 5 8 6 1 > 5

USING POSTULATES AND THEOREMS What postulate or theorem justifies the statement about the diagram? 1 4 2 7 5 8 7 4 > 5

USING POSTULATES AND THEOREMS What postulate or theorem justifies the statement about the diagram? 1 4 2 7 5 8 8 2 > 7

USING POSTULATES AND THEOREMS What postulate or theorem justifies the statement about the diagram? 1 4 2 7 5 8 9 2 and 5 are supplementary.

USING POSTULATES AND THEOREMS What postulate or theorem justifies the statement about the diagram? 1 4 2 7 5 8 10 3 > 6

USING POSTULATES AND THEOREMS What postulate or theorem justifies the statement about the diagram? 1 4 2 7 5 8 11 3 > 7

USING POSTULATES AND THEOREMS What postulate or theorem justifies the statement about the diagram? 1 4 2 7 5 8 12 1 > 8

USING POSTULATES AND THEOREMS What postulate or theorem justifies the statement about the diagram? 1 4 2 7 5 8 13 4 and 7 are supplementary.

USING PARALLEL LINES Find m 1 and m 2. Explain your reasoning. 1508 1 2

USING PARALLEL LINES Find m 1 and m 2. Explain your reasoning. 1408 1 2 1408

USING PARALLEL LINES Find m 1 and m 2. Explain your reasoning. 1228 1 2

ERROR ANALYSIS A student concludes that 9 > 10 by the Corresponding Angles Postulate. Describe and correct the error in this reasoning. 9 > 10 10 9

SHORT RESPONSE Given p i q, describe two methods you can use to show that 1 > 4. 1 3 t q p

USING PARALLEL LINES Find m 1, m 2, and m 3. Explain your reasoning. 1 2 808 3

USING PARALLEL LINES Find m 1, m 2, and m 3. Explain your reasoning. 1 2 3 1158

USING PARALLEL LINES Find m 1, m 2, and m 3. Explain your reasoning. 1 2 3 1338

ANGLES Use the diagram at the right. A B D C Name two pairs of congruent angles if ] AB and ] DC are parallel.

ANGLES Use the diagram at the right. A B D C Name two pairs of supplementary angles if ] AD and ] BC are parallel.

ALGEBRA Find the values of x and y. 458 858 x8 y

ALGEBRA Find the values of x and y. 2x8 3

ALGEBRA Find the values of x and y. x8 y8 658 558

ALGEBRA Find the values of x and y. 608 1358 (5y 2 5)8

ALGEBRA Find the values of x and y. (3y 1 2)8 528

ALGEBRA Find the values of x and y. 2y8 5x8 (14x2 10)

MULTIPLE CHOICE What is the value of y in the diagram? A 70 B 75 C 110 D 115 1108 (y 2 5)8 t n

DRAWING Draw a four-sided figure with sides}MN and }PQ , such that MN}i }PQ ,}MP i}NQ , and MNQ is an acute angle. Which angle pairs formed are congruent? Explain your reasoning.

CHALLENGE Find the values of x and y. 608 (2x 1 y)8 (2x 2 y)8

CHALLENGE Find the values of x and y. 1508 (5x 1 y)8 (5x 2 y)8

PROVING THEOREM 3.2 If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Use the steps below to write a proof of the Alternate Exterior Angles Theorem. GIVEN c p i q PROVE c 1 2 a. Show that 1 3. b. Then show that 1 2. 1 3 q p

PARKING LOT In the diagram, the lines dividing parking spaces are parallel. The measure of 1 is 1108. a. Identify the angle(s) congruent to 1. b. Find m 6. 1 2 3 4 5 6 7 8

SHORT RESPONSE The Toddler is a walking robot. Each leg of the robot has two parallel bars and a foot. When the robot walks, the leg bars remain parallel as the foot slides along the surface. a. As the legs move, are there pairs of angles that are always congruent? always supplementary? If so, which angles? b. Explain how having parallel leg bars allows the robots foot to stay flat on the floor as it moves. 1 2 5 6

EXTENDED RESPONSE You are designing a box like the one below. a. The measure of 1 is 708. What is m 2? What is m 3? b. Explain why ABC is a straight angle. c. What If? If m 1 is 608, will ABC still be a straight angle? Will the opening of the box be more steep or less steep? Explain. 1 1 2 3 3 2 B C

PROVING THEOREM 3.3 If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. Write a proof of the Consecutive Interior Angles Theorem. GIVEN c n i p PROVE c 1 and 2 are supplementary 3 2 1 p n

PROOF The Perpendicular Transversal Theorem (page 192) states that if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. Write a proof of the Perpendicular Transversal Theorem. GIVEN c t r, r i s PROVE c t s 2 1 s t

CHALLENGE In the diagram, 4 > 5. }SE bisects RSF. Find m 1. Explain your reasoning. 3 2 4 1 5 T S R E F

Find the length of each segment in the coordinate plane at the right. Which segments are congruent? (p. 15) y C(0, 23) B(3, 3) A(22, 2) 1 O 1 D(3, 0

Are angles with the given measures complementary, supplementary, or neither? (p. 35) m 1 5 628 m 2 5 1288

Are angles with the given measures complementary, supplementary, or neither? (p. 35) m 3 5 1308, m 4 5 708

Are angles with the given measures complementary, supplementary, or neither? (p. 35) m 5 5 448, m 6 5 468

Find the perimeter of the equilateral figure with the given side length. (pp. 42, 49) Pentagon, 20 cm

Find the perimeter of the equilateral figure with the given side length. (pp. 42, 49) Octagon, 2.5 ft

Find the perimeter of the equilateral figure with the given side length. (pp. 42, 49) Decagon, 33 in.

Write the converse of the statement. Is the converse true? (p. 79) Three points are collinear if they lie on the same line.

Write the converse of the statement. Is the converse true? (p. 79) If the measure of an angle is 1198, then the angle is obtuse.

VOCABULARY Draw a pair of parallel lines with a transversal. Identify all pairs of alternate exterior angles.

WRITING Use the theorems from the previous lesson and the converses of those theorems in this lesson. Write three biconditionals about parallel lines and transversals.

ALGEBRA Find the value of x that makes m i n. 1208 m n

ALGEBRA Find the value of x that makes m i n. 1358 m n (2x 1 15)8

ALGEBRA Find the value of x that makes m i n. (3x 2 15)8 1

ALGEBRA Find the value of x that makes m i n. (180 2 x)8 x

ALGEBRA Find the value of x that makes m i n. 2x8 x8 m n

ALGEBRA Find the value of x that makes m i n. 3x8 (2x 1 20)8 m

ERROR ANALYSIS A student concluded that lines a and b are parallel. Describe and correct the students error a b x y x y

IDENTIFYING PARALLEL LINES Is there enough information to prove m i n? If so, state the postulate or theorem you would use. m n

IDENTIFYING PARALLEL LINES Is there enough information to prove m i n? If so, state the postulate or theorem you would use. m n

IDENTIFYING PARALLEL LINES Is there enough information to prove m i n? If so, state the postulate or theorem you would use. n m r

IDENTIFYING PARALLEL LINES Is there enough information to prove m i n? If so, state the postulate or theorem you would use. m n

IDENTIFYING PARALLEL LINES Is there enough information to prove m i n? If so, state the postulate or theorem you would use. n m r

IDENTIFYING PARALLEL LINES Is there enough information to prove m i n? If so, state the postulate or theorem you would use. n m r

OPEN-ENDED MATH Use lined paper to draw two parallel lines cut by a transversal. Use a protractor to measure one angle. Find the measures of the other seven angles without using the protractor. Give a theorem or postulate you use to find each angle measure.

MULTI-STEP PROBLEM Complete the steps below to determine whether ] DB and ] HF are parallel. a. Find m DCG and m CGH. b. Describe the relationship between DCG and CGH. c. Are ] DB and ] HF parallel? Explain your reasoning. 778 1158 388 F E H A

PLANNING A PROOF Use these steps to plan a proof of the Consecutive Interior Angles Converse, as stated on page 162. a. Draw a diagram you can use in a proof of the theorem. b. Write the GIVEN and PROVE statements.

REASONING Can you prove that lines a and b are parallel? If so, explain how. 078 738 a

REASONING Can you prove that lines a and b are parallel? If so, explain how. 1148 488 668

REASONING Can you prove that lines a and b are parallel? If so, explain how. 1448 368 1448

ERROR ANALYSIS A student decided that ] AD i ] BC based on the diagram below. Describe and correct the students error. AD i ] BC B D C A

MULTIPLE CHOICE Use the diagram at the right. You know that 1 > 4. What can you conclude? A p i q B r i s C 2 > 3 D None of the above p s q 4 1 2 3

REASONING Use the diagram at the right for Exercises 24 and 25. 4 k 3 7 8 t 1 SHORT RESPONSE In the diagram, assume j i k. How many angle measures must be given in order to find the measure of every angle? Explain your reasoning

REASONING Use the diagram at the right for Exercises 24 and 25. 4 k 3 7 8 t 1 PLANNING A PROOF In the diagram, assume 1 and 7 are supplementary. Write a plan for a proof showing that lines j and k are parallel.

REASONING Use the diagram at the right. Which rays are parallel? Which rays are not parallel? Justify your conclusions. 588 618 628 598 A B D C F

VISUAL REASONING A point R is not in plane ABC. a. How many lines through R are perpendicular to plane ABC? b. How many lines through R are parallel to plane ABC? c. How many planes through R are parallel to plane ABC?

CHALLENGE Use the diagram. a. Find x so that p i q. b. Find y so that r i s. c. Can r be parallel to s and p be parallel to q at the same time? Explain. (x 1 56)8 (y 1 7)8 (3y 2 17)8 (

PICNIC TABLE How do you know that the top of the picnic table is parallel to the ground? p q

KITEBOARDING The diagram of the control bar of the kite shows the angles formed between the control bar and the kite lines. How do you know that n is parallel to m?

DEVELOPING PROOF Copy and complete the proof. GIVEN c m 1 5 1158, m 2 5 658 PROVE c m i n STATEMENTS REASONS 1. m 1 5 1158 and m 2 5 658 2. 1158 1 658 5 1808 3. m 1 1 m 2 5 1808 4. 1 and 2 are supplementary. 5. m i n 1. Given 2. Addition 3. ? 4. ? 5. ? n 2 1

BOWLING PINS How do you know that the bowling pins are set up in parallel lines? a b

SHORT RESPONSE The map shows part of Denver, Colorado. Use the markings on the map. Are the numbered streets parallel to one another? Explain how you can tell. PROOF Use the diagram and the given information to write a two-column or paragraph proof. E 20th Ave. E 17th Ave. E 19th Ave. E 18th Ave. Park Ave Pennsylvania St. Pearl St. Washington St. Clarkson St. Ogden St. Downing St. . Franklin St. Gilpin St. Williams St. High St.

PROOF Use the diagram and the given information to write a two-column or paragraph proof. GIVEN c 1 > 2, 3 > 4 PROVE c }AB i }CD B 2 3 4 1

PROOF Use the diagram and the given information to write a two-column or paragraph proof. GIVEN c a i b, 2 > 3 PROVE c c i d c d b a 4 3 1 2

ROOF In Exercises 36 and 37, use the diagram to write a paragraph proof. t n 5 3 6 7 8 4 1 2 PROVING THEOREM 3.5 Prove the Alternate Exterior Angles Converse.

ROOF In Exercises 36 and 37, use the diagram to write a paragraph proof. t n 5 3 6 7 8 4 1 2 PROVING THEOREM 3.6 Prove the Consecutive Interior Angles Converse.

MULTI-STEP PROBLEM Use these steps to prove Theorem 3.7, the Transitive Property of Parallel Lines. a. Copy the diagram in the Theorem box on page 164. Draw a transversal through all three lines. b. Write the GIVEN and PROVE statements. c. Use the properties of angles formed by parallel lines and transversals to prove the theorem.

EXTENDED RESPONSE Architects and engineers make drawings using a plastic triangle with angle measures 308, 608, and 908. The triangle slides along a fixed horizontal edge. a. Explain why the blue lines shown are parallel. b. Explain how the triangle can be used to draw vertical parallel lines.

REASONING Use the diagram below in Exercises 4044. How would you show that the given lines are parallel? 1148 1148 1378 668 718 668 438 a d a and b

REASONING Use the diagram below in Exercises 4044. How would you show that the given lines are parallel? 1148 1148 1378 668 718 668 438 a d b and c

REASONING Use the diagram below in Exercises 4044. How would you show that the given lines are parallel? 1148 1148 1378 668 718 668 438 a d d and f

REASONING Use the diagram below in Exercises 4044. How would you show that the given lines are parallel? 1148 1148 1378 668 718 668 438 a d e and g

REASONING Use the diagram below in Exercises 4044. How would you show that the given lines are parallel? 1148 1148 1378 668 718 668 438 a d a and c

CHALLENGE Use these steps to investigate the angle bisectors of corresponding angles. a. Construction Use a compass and straightedge or geometry drawing software to construct line l, point P not on l, and line n through P parallel to l. Construct point Q on l and construct }PQ . Choose a pair of alternate interior angles and construct their angle bisectors. b. Write a Proof Are the angle bisectors parallel? Make a conjecture. Write a proof of your conjecture.

Solve the equation. (p. 875) 3 }4 x 5 21

Solve the equation. (p. 875) 22 3 x 5 21

Solve the equation. (p. 875) 1 }5 x 5 21

Solve the equation. (p. 875) 26x 5 21

You can choose one of eight sandwich fillings and one of four kinds of bread. How many different sandwiches are possible? (p. 891)

Find the value of x if }AB > }AD and }CD > }AD . Explain your steps. (p. 112) 9x 2 11 6x 1 1

Simplify the expression. 27 2 2 8 2(24) (p. 870)

Simplify the expression. 0 } 2 (23) 1 2 6 (p. 870)

Simplify the expression. 3x 2 x 24x 1 2x (p. 139)

VOCABULARY Describe what is meant by the slope of a nonvertical line.

WRITING What happens when you apply the slope formula to a horizontal line? What happens when you apply it to a vertical line?

MATCHING Match the description of the slope of a line with its graph. A. x y B. x y C. x y D. x y m is positive.

MATCHING Match the description of the slope of a line with its graph. A. x y B. x y C. x y D. x y m is negative.

MATCHING Match the description of the slope of a line with its graph. A. x y B. x y C. x y D. x y m is zero.

MATCHING Match the description of the slope of a line with its graph. A. x y B. x y C. x y D. x y m is undefined.

FINDING SLOPE Find the slope of the line that passes through the points. (3, 5), (5, 6)

FINDING SLOPE Find the slope of the line that passes through the points. (22, 2), (2, 26)

FINDING SLOPE Find the slope of the line that passes through the points. (25, 21), (3, 21)

FINDING SLOPE Find the slope of the line that passes through the points. (2, 1), (0, 6)

ERROR ANALYSIS Describe and correct the error in finding the slope of the line. m 5 4 }3 y (6, 4) (2, 1) x 1 2 3 4

ERROR ANALYSIS Describe and correct the error in finding the slope of the line. Slope of the line through (2, 7) and (4, 5) m 5 y2 2 y }1 x2 2 x1 5} 7 2 5 4 2 2 5 2 }2 5 1

TYPES OF LINES Tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer. Line 1: (1, 0), (7, 4) Line 2: (7, 0), (3, 6)

TYPES OF LINES Tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer. Line 1: (23, 1), (27, 22) Line 2: (2, 21), (8, 4)

TYPES OF LINES Tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer. Line 1: (29, 3), (25, 7) Line 2: (211, 6), (27, 2)

GRAPHING Graph the line through the given point with the given slope. P(3, 22), slope 21 }6

GRAPHING Graph the line through the given point with the given slope. P(24, 0), slope 5 }2

GRAPHING Graph the line through the given point with the given slope. P(0, 5), slope 2 }3

STEEPNESS OF A LINE Tell which line through the given points is steeper. Line 1: (22, 3), (3, 5) Line 2: (3, 1), (6, 5)

STEEPNESS OF A LINE Tell which line through the given points is steeper. Line 1: (22, 21), (1, 22) Line 2: (25, 23), (21, 24)

STEEPNESS OF A LINE Tell which line through the given points is steeper. Line 1: (24, 2), (23, 6) Line 2: (1, 6), (3, 8)

REASONING Use your results from Exercises 19221. Describe a way to determine which of two lines is steeper without graphing them.

PERPENDICULAR LINES Find the slope of line n perpendicular to line h and passing through point P. Then copy the graph and graph line n. (23, 22) (3, 1) P(3, 23) x y

PERPENDICULAR LINES Find the slope of line n perpendicular to line h and passing through point P. Then copy the graph and graph line n. h (5, 22) (3, 4) P(6, 1) x y

PERPENDICULAR LINES Find the slope of line n perpendicular to line h and passing through point P. Then copy the graph and graph line n. (25, 23) P(24, 26) (2, 24) y x 21

REASONING Use the concept of slope to decide whether the points (23, 3), (1, 22), and (4, 0) lie on the same line. Explain your reasoning and include a diagram.

GRAPHING Graph a line with the given description. Through (0, 2) and parallel to the line through (22, 4) and (25, 1)

GRAPHING Graph a line with the given description. Through (1, 3) and perpendicular to the line through (21, 21) and (2, 0)

GRAPHING Graph a line with the given description. Through (22, 1) and parallel to the line through (3, 1) and (4, 21 }2

CHALLENGE Find the unknown coordinate so the line through the points has the given slope. (23, 2), (0, y); slope 22

CHALLENGE Find the unknown coordinate so the line through the points has the given slope. (27, 24), (x, 0); slope 1 }3

CHALLENGE Find the unknown coordinate so the line through the points has the given slope. (4, 23), (x, 1); slope 24

WATER SLIDE The water slide is 6 feet tall, and the end of the slide is 9 feet from the base of the ladder. About what slope does the slide have?

MULTIPLE CHOICE Which car has better gas mileage? A A B B C Same rate D Cannot be determined Distance driven Gas remaining B G

SHORT RESPONSE Compare the graphs of the three lines described below. Which is most steep? Which is the least steep? Include a sketch in your answer. Line a: through the point (3, 0) with a y-intercept of 4 Line b: through the point (3, 0) with a y-intercept greater than 4 Line c: through the point (3, 0) with a y-intercept between 0 and 4

MULTI-STEP PROBLEM Ladder safety guidelines include the following recommendation about ladder placement. The horizontal distance h between the base of the ladder and the object the ladder is resting against should be about one quarter of the vertical distance v between the ground and where the ladder rests against the object. a. Find the recommended slope for a ladder. b. Suppose the base of a ladder is 6 feet away from a building. The ladder has the recommended slope. Find v. c. Suppose a ladder is 34 feet from the ground where it touches a building. The ladder has the recommended slope. Find h.

MULTIPLE REPRESENTATIONS The Duquesne (pronounced du-KAYN) Incline was built in 1888 in Pittsburgh, Pennsylvania, to move people up and down a mountain there. On the incline, you move about 29 feet vertically for every 50 feet you move horizontally. When you reach the top of the hill, you have moved a horizontal distance of about 700 feet. a. Making a Table Make a table showing the vertical distance that the incline moves for each 50 feet of horizontal distance during its climb. How high is the incline at the top? b. Drawing a Graph Write a fraction that represents the slope of the inclines climb path. Draw a graph to show the climb path. c. Comparing Slopes The Burgenstock Incline in Switzerland moves about 144 vertical feet for every 271 horizontal feet. Write a fraction to represent the slope of this inclines path. Which incline is steeper, the Burgenstock or the Duquesne?

PROVING THEOREM 3.7 Use slopes of lines to write a paragraph proof of the Transitive Property of Parallel Lines on page 164.

AVERAGE RATE OF CHANGE In Exercises 39 and 40, slope can be used to describe an average rate of change. To write an average rate of change, rewrite the slope fraction so the denominator is one. BUSINESS In 2000, a business made a profit of $8500. In 2006, the business made a profit of $15,400. Find the average rate of change in dollars per year from 2000 to 2006.

AVERAGE RATE OF CHANGE In Exercises 39 and 40, slope can be used to describe an average rate of change. To write an average rate of change, rewrite the slope fraction so the denominator is one. ROCK CLIMBING A rock climber begins climbing at a point 400 feet above sea level. It takes the climber 45 minutes to climb to the destination, which is 706 feet above sea level. Find the average rate of change in feet per minute for the climber from start to finish.

EXTENDED RESPONSE The line graph shows the regular season attendance (in millions) for three professional sports organizations from 1985 to 2000. a. During which five-year period did the NBA attendance increase the most? Estimate the rate of change for this five-year period in people per year. b. During which five-year period did the NHL attendance increase the most? Estimate the rate of change for this five-year period in people per year. c. Interpret The line graph for the NFL seems to be almost linear between 1985 and 2000. Write a sentence about what this means in terms of the real-world situation. 02/&%33)/.!,30/243!44%.$!.#% .ATIONAL"ASKETBALL!SSOCIATION."! .ATIONAL&OOTBALL,EAGUE.&, .ATIONAL(OCKEY,EAGUE.(,     !TTENDANCEMILLIONS

CHALLENGE Find two values of k such that the points (23, 1), (0, k), and (k, 5) are collinear. Explain your reasoning.

Is the point (21, 27) on the line y 5 2x 2 5? Explain. (p. 878)

Find the intercepts of the graph of y 5 23x 1 9. (p. 879)

Use the diagram to write two examples of each postulate. (p. 96) P F D A C E Through any two points there exists exactly one line.

Use the diagram to write two examples of each postulate. (p. 96) P F D A C E Through any three noncollinear points there exists exactly one plane.

Solve the equation for y. Write a reason for each step. (p. 105) 6x 1 4y 5 40

Solve the equation for y. Write a reason for each step. (p. 105) }2 x 2 5 }4 y 5 210

Solve the equation for y. Write a reason for each step. (p. 105) 16 2 3y 5 24x

VOCABULARY What does intercept mean in the expression slope-intercept form?

WRITING Explain how you can use the standard form of a linear equation to find the intercepts of a line.

WRITING EQUATIONS Write an equation of the line shown. (3, 0) (0, 24) x y 1

WRITING EQUATIONS Write an equation of the line shown. (0, 22) (25, 23) x y 1

WRITING EQUATIONS Write an equation of the line shown. (23, 4) x y 1 1

WRITING EQUATIONS Write an equation of the line shown. x y (2, 23) 1 1 (

WRITING EQUATIONS Write an equation of the line shown. y (5, 6) (1, 0

WRITING EQUATIONS Write an equation of the line shown. y (1, 23) (25, 21

MULTIPLE CHOICE Which equation is an equation of the line in the graph? A y 5 21 }2x B y 5 21 }2x 1 1 C y 5 22x D y 5 22x 1 1 (22, 2) x y 4 22 1

WRITING EQUATIONS Write an equation of the line with the given slope m and y-intercept b. m 5 25, b 5 212

WRITING EQUATIONS Write an equation of the line with the given slope m and y-intercept b. m 5 3, b 5 2

WRITING EQUATIONS Write an equation of the line with the given slope m and y-intercept b. m 5 4, b 5 26

WRITING EQUATIONS Write an equation of the line with the given slope m and y-intercept b. m 5 25 }2 , b 5 0

WRITING EQUATIONS Write an equation of the line with the given slope m and y-intercept b. m 5 4 }9 , b 5 22 }9

WRITING EQUATIONS Write an equation of the line with the given slope m and y-intercept b. m 5 211 }5 , b 5 212

WRITING EQUATIONS Write an equation of the line that passes through the given point P and has the given slope m. P(21, 0), m 5 21

WRITING EQUATIONS Write an equation of the line that passes through the given point P and has the given slope m. P(5, 4), m 5 4

WRITING EQUATIONS Write an equation of the line that passes through the given point P and has the given slope m. P(6, 22), m 5 3

WRITING EQUATIONS Write an equation of the line that passes through the given point P and has the given slope m. P(28, 22), m 5 22 }3

WRITING EQUATIONS Write an equation of the line that passes through the given point P and has the given slope m. P(0, 23), m 5 21 }6

WRITING EQUATIONS Write an equation of the line that passes through the given point P and has the given slope m. P(213, 7), m 5 0

WRITING EQUATIONS Write an equation of a line with undefined slope that passes through the point (3, 22).

PARALLEL LINES Write an equation of the line that passes through point P and is parallel to the line with the given equation. P(0, 21), y 5 22x 1 3

PARALLEL LINES Write an equation of the line that passes through point P and is parallel to the line with the given equation. P(27, 24), y 5 16

PARALLEL LINES Write an equation of the line that passes through point P and is parallel to the line with the given equation. P(3, 8), y 2 1 5 1 }5 (x 1 4)

PARALLEL LINES Write an equation of the line that passes through point P and is parallel to the line with the given equation. P(22, 6), x 5 25

PARALLEL LINES Write an equation of the line that passes through point P and is parallel to the line with the given equation. P(22, 1), 10x 1 4y 5 28

PARALLEL LINES Write an equation of the line that passes through point P and is parallel to the line with the given equation. P(4, 0), 2x 1 2y 5 12

MULTIPLE CHOICE Line a passes through points (22, 1) and (2, 9). Which equation is an equation of a line parallel to line a? A y 5 22x 1 5 B y 5 21 }2x 1 5 C y 5 1 }2 x 2 5 D y 5 2x 2 5

PERPENDICULAR LINES Write an equation of the line that passes through point P and is perpendicular to the line with the given equation. P(0, 0), y 5 29x 2 1

PERPENDICULAR LINES Write an equation of the line that passes through point P and is perpendicular to the line with the given equation. P(21, 1), y 5 7 }3 x 1 10

PERPENDICULAR LINES Write an equation of the line that passes through point P and is perpendicular to the line with the given equation. P(4, 26), y 5 23

PERPENDICULAR LINES Write an equation of the line that passes through point P and is perpendicular to the line with the given equation. P(2, 3), y 2 4 5 22(x 1 3)

PERPENDICULAR LINES Write an equation of the line that passes through point P and is perpendicular to the line with the given equation. P(0, 25), x 5 20

PERPENDICULAR LINES Write an equation of the line that passes through point P and is perpendicular to the line with the given equation. P(28, 0), 3x 2 5y 5 6

GRAPHING EQUATIONS Graph the equation. 8x 1 2y 5 210

GRAPHING EQUATIONS Graph the equation. x 1 y 5 1

GRAPHING EQUATIONS Graph the equation. 4x 2 y 5 28

GRAPHING EQUATIONS Graph the equation. 2x 1 3y 5 29

GRAPHING EQUATIONS Graph the equation. y 2 2 5 21

GRAPHING EQUATIONS Graph the equation. y 1 2 5 x 2 1

GRAPHING EQUATIONS Graph the equation. x 1 3 5 24

GRAPHING EQUATIONS Graph the equation. 2y 2 4 5 2x 1 1

GRAPHING EQUATIONS Graph the equation. 3(x 2 2) 5 2y 2 4

ERROR ANALYSIS Describe and correct the error in finding the x- and y-intercepts of the graph of 5x 2 3y 5 215. To find the x-intercept, let x 5 0: 5x 2 3y 5 215 5(0) 2 3y 5 215 y 5 5 To find the y-intercept, let y 5 0: 5x 2 3y 5 215 5x 2 3(0) 5 215 x 5 23

IDENTIFYING PARALLEL LINES Which lines are parallel, if any? y 5 3x 2 4 x 1 3y 5 6 3(x 1 1) 5 y 2 2

IDENTIFYING PARALLEL LINES Which lines are parallel, if any? x 1 2y 5 9 y 5 0.5 x 1 7 2x 1 2y 5 25

IDENTIFYING PARALLEL LINES Which lines are parallel, if any? x 2 6y 5 10 6x 2 y 5 11 x 1 6y 5 12

USING INTERCEPTS Identify the x- and y-intercepts of the line. Use the intercepts to write an equation of the line. . x y 1 1

USING INTERCEPTS Identify the x- and y-intercepts of the line. Use the intercepts to write an equation of the line. y 21 1

USING INTERCEPTS Identify the x- and y-intercepts of the line. Use the intercepts to write an equation of the line. y 20 10

INTERCEPTS A line passes through the points (210, 23) and (6, 1). Where does the line intersect the x-axis? Where does the line intersect the y-axis?

SOLUTIONS TO EQUATIONS Graph the linear equations. Then use the graph to estimate how many solutions the equations share. y 5 4x 1 9 4x 2 y 5 1

SOLUTIONS TO EQUATIONS Graph the linear equations. Then use the graph to estimate how many solutions the equations share. 3y 1 4x 5 16 2x 2 y 5 18

SOLUTIONS TO EQUATIONS Graph the linear equations. Then use the graph to estimate how many solutions the equations share. y 5 25x 1 6 10x 1 2y 5 12

ALGEBRA Solve Exercises 5355 algebraically. (For help, see Skills Review Handbook, p. 880.) Make a conjecture about how the solution(s) can tell you whether the lines intersect, are parallel, or are the same line.

LGEBRA Find a value for k so that the line through (21, k) and (27, 22) is parallel to the line with equation y 5 x 1 1.

ALGEBRA Find a value for k so that the line through (k, 2) and (7, 0) is perpendicular to the line with equation y 5 x 2 28 }5 .

CHALLENGE Graph the points R(27, 23), S(22, 3), and T(10, 27). Connect them to make nRST. Write an equation of the line containing each side. Explain how you can use slopes to show that nRST has one right angle.

WEB HOSTING The graph models the total cost of using a web hosting service for several months. Write an equation of the line. Tell what the slope and y-intercept mean in this situation. Then find the total cost of using the web hosting service for one year. Web Hosting Cost (dollars) 2 4 6 8 10 12 300 200 100 0 0 x y (0, 50) (10, 280)

SCIENCE Scientists believe that a Tyrannosaurus Rex weighed about 2000 kilograms by age 14. It then had a growth spurt for four years, gaining 2.1 kilograms per day. Write an equation to model this situation. What are the slope and y-intercept? Tell what the slope and y-intercept mean in this situation. Field Museum, Chicago, Illinois

MULTI-STEP PROBLEM A national park has two options: a $50 pass for all admissions during the year, or a $4 entrance fee each time you enter. a. Model Write an equation to model the cost of going to the park for a year using a pass and another equation for paying a fee each time. b. Graph Graph both equations you wrote in part (a). c. Interpret How many visits do you need to make for the pass to be cheaper? Explain.

PIZZA COSTS You are buying slices of pizza for you and your friends. A small slice costs $2 and a large slice costs $3. You have $24 to spend. Write an equation in standard form Ax 1 By 5 C that models this situation. What do the values of A, B, and C mean in this situation?

SHORT RESPONSE You run at a rate of 4 miles per hour and your friend runs at a rate of 3.5 miles per hour. Your friend starts running 10 minutes before you, and you run for a half hour on the same path. Will you catch up to your friend? Use a graph to support your answer.

EXTENDED RESPONSE Audrey and Sara are making jewelry. Audrey buys 2 bags of beads and 1 package of clasps for a total of $13. Sara buys 5 bags of beads and 2 packages of clasps for a total of $27.50. a. Let b be the price of one bag of beads and let c be the price of one package of clasps. Write equations to represent the total cost for Audrey and the total cost for Sara. b. Graph the equations from part (a). c. Explain the meaning of the intersection of the two lines in terms of the real-world situation.

CHALLENGE Michael is deciding which gym membership to buy. Points (2, 112) and (4, 174) give the cost of gym membership at one gym after two and four months. Points (1, 62) and (3, 102) give the cost of gym membership at a second gym after one and three months. Write equations to model the cost of each gym membership. At what point do the graphs intersect, if they intersect? Which gym is cheaper? Explain.

Find the length of each segment. Round to the nearest tenth of a unit. (p. 15) y 1 1 B(4, 2) A(1, 4)

Find the length of each segment. Round to the nearest tenth of a unit. (p. 15) N(2, 0) M(23, 23) x y

Find the length of each segment. Round to the nearest tenth of a unit. (p. 15) S(1, 1) T(6, 23) x y 1

Describe the pattern in the numbers. Write the next number in the pattern. (p. 72) 22, 27, 212, 217, . . .

Describe the pattern in the numbers. Write the next number in the pattern. (p. 72) 4, 8, 16, 32, . . .

Describe the pattern in the numbers. Write the next number in the pattern. (p. 72) 101, 98, 95, 92, . . .

Find m 1 and m 2. Explain your reasoning. (p. 154) 828 n m 1

Find m 1 and m 2. Explain your reasoning. (p. 154) 648 n m 1 2

Find m 1 and m 2. Explain your reasoning. (p. 154) 1578 n m 2

VOCABULARY The length of which segment shown is called the distance between the two parallel lines? Explain.

JUSTIFYING STATEMENTS Write the theorem that justifies the statement. j k j k 1 2

JUSTIFYING STATEMENTS Write the theorem that justifies the statement. 4 and 5 are complementary. 5 4

JUSTIFYING STATEMENTS Write the theorem that justifies the statement. 1 and 2 are right angles. 2 1

APPLYING THEOREMS Find m 1. 658

APPLYING THEOREMS Find m 1. 1

APPLYING THEOREMS Find m 1. 1 388

SHOWING LINES PARALLEL Explain how you would show that m i n. n m

SHOWING LINES PARALLEL Explain how you would show that m i n. n m x8 x8

SHOWING LINES PARALLEL Explain how you would show that m i n. n m x8 x

SHORT RESPONSE Explain how to draw two parallel lines using only a straightedge and a protractor.

SHORT RESPONSE Describe how you can fold a sheet of paper to create two parallel lines that are perpendicular to the same line.

ERROR ANALYSIS Explain why the statement about the figure is incorrect. x y Lines y and z are parallel.

ERROR ANALYSIS Explain why the statement about the figure is incorrect. 12 cm 60 A B C The distance from ] AB to point C is 12 cm.

FINDING ANGLE MEASURES In the diagram, ] FG ] GH . Find the value of x. F G H 638 (x 1 14)8

FINDING ANGLE MEASURES In the diagram, ] FG ] GH . Find the value of x. 08 (x 2 25)8

FINDING ANGLE MEASURES In the diagram, ] FG ] GH . Find the value of x. H G x8

DRAWING CONCLUSIONS Determine which lines, if any, must be parallel. Explain your reasoning. m k n p

DRAWING CONCLUSIONS Determine which lines, if any, must be parallel. Explain your reasoning. d f g

DRAWING CONCLUSIONS Determine which lines, if any, must be parallel. Explain your reasoning. v w y

MULTIPLE CHOICE Which statement must be true if c d? A m 1 1 m 2 5 908 B m 1 1 m 2 < 908 C m 1 1 m 2 > 908 D Cannot be determined 2 1 c

WRITING Explain why the distance between two lines is only defined for parallel lines.

FINDING DISTANCES Use the Distance Formula to find the distance between the two parallel lines. Round to the nearest tenth, if necessary. x y

FINDING DISTANCES Use the Distance Formula to find the distance between the two parallel lines. Round to the nearest tenth, if necessary. 1 1

CONSTRUCTION You are given a line n and a point P not on n. Use a compass to find two points on n equidistant from P. Then use the steps for the construction of a segment bisector (page 33) to construct a line perpendicular to n through P.

FINDING ANGLES Find all the unknown angle measures in the diagram at the right. Justify your reasoning for each angle measure. 2 5 4 1 3 308 40

FINDING DISTANCES Find the distance between the lines with the equations y 5 3 }2 x 1 4 and 23x 1 2y 5 21.

CHALLENGE Describe how you would find the distance from a point to a plane. Can you find the distance from a line to a plane? Explain.

STREAMS You are trying to cross a stream from point A. Which point should you jump to in order to jump the shortest distance? Explain. B E

SHORT RESPONSE The segments that form the path of a crosswalk are usually perpendicular to the crosswalk. Sketch what the segments would look like if they were perpendicular to the crosswalk. Which method requires less paint? Explain.

PROVING THEOREM 3.8 Copy and complete the proof that if two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. GIVEN c 1 and 2 are a linear pair. 1 > 2 PROVE c g h STATEMENTS REASONS 1. 1 and 2 are a linear pair. 2. 1 and 2 are supplementary. 3. ? 4. 1 > 2 5. m 1 5 m 2 6. m 1 1 m 1 5 1808 7. 2(m 1) 5 1808 8. m 1 5 908 9. ? 10. g h 1. Given 2. ? 3. Definition of supplementary angles 4. Given 5. ? 6. Substitution Property of Equality 7. Combine like terms. 8. ? 9. Definition of a right angle 10. ? g h 1 2

PROVING THEOREMS Write a proof of the given theorem. Theorem 3.9

PROVING THEOREMS Write a proof of the given theorem. Theorem 3.11, Perpendicular Transversal Theorem

PROVING THEOREMS Write a proof of the given theorem. Theorem 3.12, Lines Perpendicular to a Transversal Theorem

CHALLENGE Suppose the given statement is true. Determine whether ] AB ] AC . 4 A B C 1 and 2 are congruent.

CHALLENGE Suppose the given statement is true. Determine whether ] AB ] AC . 4 A B C 3 and 4 are complementary.

CHALLENGE Suppose the given statement is true. Determine whether ] AB ] AC . 4 A B C m 1 5 m 3 and m 2 5 m 4

CHALLENGE Suppose the given statement is true. Determine whether ] AB ] AC . 4 A B C m 1 5 408 and m 4 5 508

Find the value of x. (p. 24) 308 458

Find the value of x. (p. 24) x8 608

Find the value of x. (p. 24) 238 878 x8

Find the circumference and area of the circle. Round to the nearest tenth. (p. 49) 20 m

Find the circumference and area of the circle. Round to the nearest tenth. (p. 49) 12 in.

Find the circumference and area of the circle. Round to the nearest tenth. (p. 49) 9 cm

Find the value of x that makes m i n. (p. 161) n m x8 4

Find the value of x that makes m i n. (p. 161) n m 8x8 1

Find the value of x that makes m i n. (p. 161) n m (x 1 30)8 12

Copy and complete: Two lines that do not intersect and are not coplanar are called ? .

WRITING Compare alternate interior angle pairs and consecutive interior angle pairs.

Copy and complete the statement using the figure at the right. 2 1 4 3 6 8 5 7 1 and ? are corresponding angles.

Copy and complete the statement using the figure at the right. 2 1 4 3 6 8 5 7 3 and ? are alternate interior angles.

Copy and complete the statement using the figure at the right. 2 1 4 3 6 8 5 7 4 and ? are consecutive interior angles.

Copy and complete the statement using the figure at the right. 2 1 4 3 6 8 5 7 7 and ? are alternate exterior angles.

Identify the form of the equation as slope-intercept form or standard form. 14x 2 2y 5 26

Identify the form of the equation as slope-intercept form or standard form. 5 7x 2 13

Think of each segment in the diagram of a rectangular box as part of a line. Which line(s) or plane(s) contain point N and appear to fit the description? J K R M N P Line(s) perpendicular to ] QR

Think of each segment in the diagram of a rectangular box as part of a line. Which line(s) or plane(s) contain point N and appear to fit the description? J K R M N P Line(s) parallel to ] QR

Think of each segment in the diagram of a rectangular box as part of a line. Which line(s) or plane(s) contain point N and appear to fit the description? J K R M N P Line(s) skew to ] QR

Think of each segment in the diagram of a rectangular box as part of a line. Which line(s) or plane(s) contain point N and appear to fit the description? J K R M N P Plane(s) parallel to plane LMQ

Find m 1 and m 2. Explain your reasoning. 2 1 5

Find m 1 and m 2. Explain your reasoning. 1 958

Find m 1 and m 2. Explain your reasoning. 1358 1

Find the values of x and y. 8 358 y

Find the values of x and y. (5x 2 17)8 488 y8

Find the values of x and y. 2y8 588

FLAG OF PUERTO RICO Sketch the rectangular flag of Puerto Rico as shown at the right. Find the measure of 1 if m 3 5 558. Justify each step in your argument.   

Find the value of x that makes m i n. x8 738 n m

Find the value of x that makes m i n. 1478 n m (x 1 14)8

Find the value of x that makes m i n. (2x 1 20)8

Tell whether the lines through the given points are parallel, perpendicular, or neither. Line 1: (8, 12), (7, 25) Line 2: (29, 3), (8, 2)

Tell whether the lines through the given points are parallel, perpendicular, or neither. Line 1: (3, 24), (21, 4) Line 2: (2, 7), (5, 1)

Write equations of the lines that pass through point P and are (a) parallel and (b) perpendicular to the line with the given equation. P(3, 21), y 5 6x 2 4

Write equations of the lines that pass through point P and are (a) parallel and (b) perpendicular to the line with the given equation. P(26, 5), 7y 1 4x 5 2

Use the Distance Formula to find the distance between the two parallel lines. Round to the nearest tenth, if necessary. y (0, 6) (21, 3) (2, 2) 1 2

Use the Distance Formula to find the distance between the two parallel lines. Round to the nearest tenth, if necessary. y (0, 1) (22, 6) (3, 8)