 6.6.2.1: VOCABULARY Copy and complete: A ? is a drawing that has the same sh...
 6.1: Copy and complete the statement. A ? is a transformation in which t...
 6.6.3.1: VOCABULARY Copy and complete: Two polygons are similar if correspon...
 6.6.4.1: VOCABULARY Copy and complete: If two angles of one triangle are con...
 6.6.5.1: VOCABULARY You plan to prove that nACB is similar to nPXQ by the SS...
 6.6.1.1: VOCABULARY Copy the proportion m }n 5 p }q . Identify the means of ...
 6.6.6.1: VOCABULARY State the Triangle Proportionality Theorem. Draw a diagram.
 6.6.7.1: VOCABULARY Copy and complete: In a dilation, the image is ? to the ...
 6.6.2.2: WRITING Suppose the scale of a model of the Eiffel Tower is 1 inch ...
 6.2: Copy and complete the statement. If nPQR , nXYZ, then PQ}XY 5 ?}YZ ...
 6.6.3.2: WRITING If two polygons are congruent, must they be similar? If two...
 6.6.4.2: WRITING Can you assume that corresponding sides and corresponding a...
 6.6.5.2: WRITING If you know two triangles are similar by the SAS Similarity...
 6.6.1.2: WRITING Write three ratios that are equivalent to the ratio 3 : 4. ...
 6.6.6.2: WRITING Compare the Midsegment Theorem (see page 295) and the Trian...
 6.6.7.2: WRITING Explain how to find the scale factor of a dilation. How do ...
 6.6.2.3: REASONING Copy and complete the statement. If 8}x 53}y, then 8}3 5?}?
 6.3: Copy and complete the statement. WRITING Describe the relationship ...
 6.6.3.3: USING SIMILARITY List all pairs of congruent angles for the figures...
 6.6.4.3: REASONING Use the diagram to complete the statement. A CE25 15 F Dx...
 6.6.5.3: SSS SIMILARITY THEOREM Verify that nABC , nDEF. Find the scale fact...
 6.6.1.3: SIMPLIFYING RATIOS Simplify the ratio. $20 : $5
 6.6.6.3: FINDING THE LENGTH OF A SEGMENT Find the length of}AB 4123CB DA
 6.6.7.3: DRAWING DILATIONS Draw a dilation of the polygon with the given ver...
 6.6.2.4: REASONING Copy and complete the statement. If x}9 5y}20 , then x}y ...
 6.4: The length of a rectangle is 20 meters and the width is 15 meters. ...
 6.6.3.4: USING SIMILARITY List all pairs of congruent angles for the figures...
 6.6.4.4: REASONING Use the diagram to complete the statement. A CE25 15 F Dx...
 6.6.5.4: SSS SIMILARITY THEOREM Verify that nABC , nDEF. Find the scale fact...
 6.6.1.4: SIMPLIFYING RATIOS Simplify the ratio. 15 cm212 cm2
 6.6.6.4: FINDING THE LENGTH OF A SEGMENT Find the length of}AB 1412D CE BA
 6.6.7.4: DRAWING DILATIONS Draw a dilation of the polygon with the given ver...
 6.6.2.5: REASONING Copy and complete the statement. If x}6 5y}15 , then x}1 ...
 6.5: The measures of the angles in nUVW are in the extended ratio of 1 :...
 6.6.3.5: USING SIMILARITY List all pairs of congruent angles for the figures...
 6.6.4.5: REASONING Use the diagram to complete the statement. A CE25 15 F Dx...
 6.6.5.5: SSS SIMILARITY THEOREM Is either nJKL or nRST similar to nABC? B 8 ...
 6.6.1.5: SIMPLIFYING RATIOS Simplify the ratio. 6 L : 10 mL
 6.6.6.5: REASONING Use the given information to determine whether}KM i }JN ....
 6.6.7.5: DRAWING DILATIONS Draw a dilation of the polygon with the given ver...
 6.6.2.6: REASONING Copy and complete the statement. If 14}3 5x}y, then 17}3 ...
 6.6: Find the geometric mean of 8 and 12.
 6.6.3.6: MULTIPLE CHOICE Triangles ABC and DEF are similar. Which statement ...
 6.6.4.6: REASONING Use the diagram to complete the statement. A CE25 15 F Dx...
 6.6.5.6: SSS SIMILARITY THEOREM Is either n JKL or nRST similar to nABC? STA...
 6.6.1.6: SIMPLIFYING RATIOS Simplify the ratio. 1 mi20 ft
 6.6.6.6: REASONING Use the given information to determine whether}KM i }JN ....
 6.6.7.6: DRAWING DILATIONS Draw a dilation of the polygon with the given ver...
 6.6.2.7: REASONING Decide whether the statement is true or false. If 8}m 5n}...
 6.7: Use the diagram and the given information to find the unknown lengt...
 6.6.3.7: DETERMINING SIMILARITY Determine whether the polygons are similar. ...
 6.6.4.7: REASONING Use the diagram to complete the statement. A CE25 15 F Dx...
 6.6.5.7: SAS SIMILARITY THEOREM Determine whether the two triangles are simi...
 6.6.1.7: SIMPLIFYING RATIOS Simplify the ratio. 7 ft12 in
 6.6.6.7: REASONING Use the given information to determine whether}KM i }JN ....
 6.6.7.7: DRAWING DILATIONS Draw a dilation of the polygon with the given ver...
 6.6.2.8: REASONING Decide whether the statement is true or false. If 5}7 5a}...
 6.8: Use the diagram and the given information to find the unknown lengt...
 6.6.3.8: DETERMINING SIMILARITY Determine whether the polygons are similar. ...
 6.6.4.8: REASONING Use the diagram to complete the statement. A CE25 15 F Dx...
 6.6.5.8: SAS SIMILARITY THEOREM Determine whether the two triangles are simi...
 6.6.1.8: SIMPLIFYING RATIOS Simplify the ratio. 80 cm2 m
 6.6.6.8: MULTIPLE CHOICE For the figure at the right, which statement is not...
 6.6.7.8: DRAWING DILATIONS Draw a dilation of the polygon with the given ver...
 6.6.2.9: REASONING Decide whether the statement is true or false. If d}2 5g}...
 6.9: In Exercises 9 and 10, determine whether the polygons are similar. ...
 6.6.3.9: USING SIMILAR POLYGONS In the diagram, JKLM , EFGH. KJMx L30 320658...
 6.6.4.9: AA SIMILARITY POSTULATE In Exercises 914, determine whether the tri...
 6.6.5.9: ALGEBRA Find the value of n that makes nPQR , nXYZ when PQ 5 4, QR ...
 6.6.1.9: SIMPLIFYING RATIOS Simplify the ratio. 3 lb10 oz
 6.6.6.9: ALGEBRA Find the value of the variable. 52114
 6.6.7.9: IDENTIFYING DILATIONS Determine whether the dilation from Figure A ...
 6.6.2.10: REASONING Decide whether the statement is true or false. f 4}1 x4 5...
 6.10: In Exercises 9 and 10, determine whether the polygons are similar. ...
 6.6.3.10: USING SIMILAR POLYGONS In the diagram, JKLM , EFGH. KJMx L30 320658...
 6.6.4.10: AA SIMILARITY POSTULATE In Exercises 914, determine whether the tri...
 6.6.5.10: SHOWING SIMILARITY Show that the triangles are similar and write a ...
 6.6.1.10: SIMPLIFYING RATIOS Simplify the ratio. 2 gallons18 quarts
 6.6.6.10: ALGEBRA Find the value of the variable. 84 6
 6.6.7.10: IDENTIFYING DILATIONS Determine whether the dilation from Figure A ...
 6.6.2.11: PROPERTIES OF PROPORTIONS Use the diagram and the given information...
 6.11: POSTERS Two similar posters have a scale factor of 4 : 5. The large...
 6.6.3.11: USING SIMILAR POLYGONS In the diagram, JKLM , EFGH. KJMx L30 320658...
 6.6.4.11: AA SIMILARITY POSTULATE In Exercises 914, determine whether the tri...
 6.6.5.11: SHOWING SIMILARITY Show that the triangles are similar and write a ...
 6.6.1.11: WRITING RATIOS Find the ratio of the width to the length of the rec...
 6.6.6.11: ALGEBRA Find the value of the variable. z34.51.5
 6.6.7.11: IDENTIFYING DILATIONS Determine whether the dilation from Figure A ...
 6.6.2.12: PROPERTIES OF PROPORTIONS Use the diagram and the given information...
 6.12: Use the AA Similarity Postulate to show that the triangles are simi...
 6.6.3.12: PERIMETER Two similar FOR SALE signs have a scale factor of 5 : 3. ...
 6.6.4.12: AA SIMILARITY POSTULATE In Exercises 914, determine whether the tri...
 6.6.5.12: SHOWING SIMILARITY Show that the triangles are similar and write a ...
 6.6.1.12: WRITING RATIOS Find the ratio of the width to the length of the rec...
 6.6.6.12: ERROR ANALYSIS A student begins to solve for the length of }AD as s...
 6.6.7.12: IDENTIFYING DILATIONS Determine whether the dilation from Figure A ...
 6.6.2.13: SCALE DIAGRAMS In Exercises 13 and 14, use the diagram of the field...
 6.13: Use the AA Similarity Postulate to show that the triangles are simi...
 6.6.3.13: ERROR ANALYSIS The triangles are similar. Describe and correct the ...
 6.6.4.13: AA SIMILARITY POSTULATE In Exercises 914, determine whether the tri...
 6.6.5.13: ERROR ANALYSIS Describe and correct the students error in writing t...
 6.6.1.13: WRITING RATIOS Find the ratio of the width to the length of the rec...
 6.6.6.13: MULTIPLE CHOICE Find the value of x. A 1 }2 B 1 C 2 D 3 2x2x 1 16x6...
 6.6.7.13: MULTIPLE CHOICE You want to create a quadrilateral PQRS that is sim...
 6.6.2.14: SCALE DIAGRAMS In Exercises 13 and 14, use the diagram of the field...
 6.14: CELL TOWER A cellular telephone tower casts a shadow that is 72 fee...
 6.6.3.14: REASONING Are the polygons always, sometimes, or never similar? Two...
 6.6.4.14: AA SIMILARITY POSTULATE In Exercises 914, determine whether the tri...
 6.6.5.14: MULTIPLE CHOICE In the diagram, } MN MR 5 } MP MQ . Which of the st...
 6.6.1.14: FINDING RATIOS Use the number line to find the ratio of the distanc...
 6.6.6.14: ALGEBRA Find the value of the variable. 16.511 29
 6.6.7.14: ERROR ANALYSIS A student found the scale factor of the dilation fro...
 6.6.2.15: ERROR ANALYSIS Describe and correct the error made in the reasoning...
 6.15: Use the SSS Similarity Theorem or SAS Similarity Theorem to show th...
 6.6.3.15: REASONING Are the polygons always, sometimes, or never similar? Two...
 6.6.4.15: ERROR ANALYSIS Explain why the students similarity statement is inc...
 6.6.5.15: DRAWING TRIANGLES Sketch the triangles using the given description....
 6.6.1.15: FINDING RATIOS Use the number line to find the ratio of the distanc...
 6.6.6.15: ALGEBRA Find the value of the variable. q 36281
 6.6.7.15: ERROR ANALYSIS A student says that the figure shown represents a di...
 6.6.2.16: PROPERTIES OF PROPORTIONS Use the diagram and the given information...
 6.16: Use the SSS Similarity Theorem or SAS Similarity Theorem to show th...
 6.6.3.16: REASONING Are the polygons always, sometimes, or never similar? A r...
 6.6.4.16: MULTIPLE CHOICE What is the value of p? A 5 B 20 C 28.8 D Cannot be...
 6.6.5.16: DRAWING TRIANGLES Sketch the triangles using the given description....
 6.6.1.16: FINDING RATIOS Use the number line to find the ratio of the distanc...
 6.6.6.16: FINDING SEGMENT LENGTHS Use the diagram to find the value of each v...
 6.6.7.16: IDENTIFYING TRANSFORMATIONS Determine whether the transformation sh...
 6.6.2.17: PROPERTIES OF PROPORTIONS Use the diagram and the given information...
 6.17: Use the given information to determine whether}AB i }CD . 820 1610C
 6.6.3.17: REASONING Are the polygons always, sometimes, or never similar? A s...
 6.6.4.17: ERROR ANALYSIS A student uses the proportion 4 }6 5 5 }x to find th...
 6.6.5.17: DRAWING TRIANGLES Sketch the triangles using the given description....
 6.6.1.17: FINDING RATIOS Use the number line to find the ratio of the distanc...
 6.6.6.17: FINDING SEGMENT LENGTHS Use the diagram to find the value of each v...
 6.6.7.17: IDENTIFYING TRANSFORMATIONS Determine whether the transformation sh...
 6.6.2.18: MULTIPLE CHOICE If x, y, z, and q are four different numbers, and t...
 6.18: Use the given information to determine whether}AB i }CD . 3.522.51220C
 6.6.3.18: SHORT RESPONSE The scale factor of Figure A to Figure B is 1 : x. W...
 6.6.4.18: OPENENDED MATH In Exercises 18 and 19, make a sketch that can be u...
 6.6.5.18: FINDING MEASURES In Exercises 1823, use the diagram to copy and com...
 6.6.1.18: PERIMETER The perimeter of a rectangle is 154 feet. The ratio of th...
 6.6.6.18: RROR ANALYSIS A student claims that AB 5 AC using the method shown....
 6.6.7.18: IDENTIFYING TRANSFORMATIONS Determine whether the transformation sh...
 6.6.2.19: CHALLENGE Two number patterns are proportional if there is a nonzer...
 6.19: Draw a dilation of the polygon with the given vertices using the gi...
 6.6.3.19: SIMILAR TRIANGLES Identify the type of special segment shown in blu...
 6.6.4.19: OPENENDED MATH In Exercises 18 and 19, make a sketch that can be u...
 6.6.5.19: FINDING MEASURES In Exercises 1823, use the diagram to copy and com...
 6.6.1.19: SEGMENT LENGTHS In the diagram, AB:BC is 2 : 7 and AC 5 36. Find AB...
 6.6.6.19: CONSTRUCTION Follow the instructions for constructing a line segmen...
 6.6.7.19: FINDING SCALE FACTORS Find the scale factor of the dilation of Figu...
 6.6.2.20: CHALLENGE Two number patterns are proportional if there is a nonzer...
 6.20: Draw a dilation of the polygon with the given vertices using the gi...
 6.6.3.20: SIMILAR TRIANGLES Identify the type of special segment shown in blu...
 6.6.4.20: MULTIPLE CHOICE In the figure at the right, find the length of }BD ...
 6.6.5.20: FINDING MEASURES In Exercises 1823, use the diagram to copy and com...
 6.6.1.20: USING EXTENDED RATIOS The measures of the angles of a triangle are ...
 6.6.6.20: CHALLENGE Given segments with lengths r, s, and t, construct a segm...
 6.6.7.20: FINDING SCALE FACTORS Find the scale factor of the dilation of Figu...
 6.6.2.21: CHALLENGE Two number patterns are proportional if there is a nonzer...
 6.21: Draw a dilation of the polygon with the given vertices using the gi...
 6.6.3.21: USING SCALE FACTOR Triangles NPQ and RST are similar. The side leng...
 6.6.4.21: ALGEBRA Find coordinates for point E so that nABC S nADE. DBA CE A(...
 6.6.5.21: FINDING MEASURES In Exercises 1823, use the diagram to copy and com...
 6.6.1.21: USING EXTENDED RATIOS The measures of the angles of a triangle are ...
 6.6.6.21: CITY MAP On the map below, Idaho Avenue bisects the angle between U...
 6.6.7.21: MULTIPLE CHOICE In the diagram shown, nABO is a dilation of nDEO. T...
 6.6.2.22: ARCHITECTURE A basket manufacturer has headquarters in an office bu...
 6.6.3.22: USING SCALE FACTOR Triangles NPQ and RST are similar. The side leng...
 6.6.4.22: ALGEBRA Find coordinates for point E so that nABC S nADE. DBA CE A(...
 6.6.5.22: FINDING MEASURES In Exercises 1823, use the diagram to copy and com...
 6.6.1.22: USING EXTENDED RATIOS The measures of the angles of a triangle are ...
 6.6.6.22: PROVING THEOREM 6.4 Prove the Triangle Proportionality Theorem. GIV...
 6.6.7.22: SHORT RESPONSE Suppose you dilate a figure using a scale factor of ...
 6.6.2.23: MAP SCALE A street on a map is 3 inches long. The actual street is ...
 6.6.3.23: USING SIMILAR TRIANGLES In the diagram, nABC , nDEF. D FEB19 4510 2...
 6.6.4.23: ALGEBRA Find coordinates for point E so that nABC S nADE. DBA CE A(...
 6.6.5.23: FINDING MEASURES In Exercises 1823, use the diagram to copy and com...
 6.6.1.23: ALGEBRA Solve the proportion. 6}x 5 3}2
 6.6.6.23: PROVING THEOREM 6.6 Use the diagram with the auxiliary line drawn t...
 6.6.7.23: CHALLENGE Describe the two transformations, the first followed by t...
 6.6.2.24: MULTIPLE CHOICE A model train engine is 12 centimeters long. The ac...
 6.6.3.24: USING SIMILAR TRIANGLES In the diagram, nABC , nDEF. D FEB19 4510 2...
 6.6.4.24: ALGEBRA Find coordinates for point E so that nABC S nADE. DBA CE A(...
 6.6.5.24: SIMILAR TRIANGLES In the diagram at the right, name the three pairs...
 6.6.1.24: ALGEBRA Solve the proportion. y}20 5 3}10
 6.6.6.24: MULTISTEP PROBLEM The real estate term lake frontage refers to the...
 6.6.7.24: CHALLENGE Describe the two transformations, the first followed by t...
 6.6.7.25: BILLBOARD ADVERTISEMENT A billboard advertising agency requires eac...
 6.6.2.25: MAP READING The map of a hiking trail has a scale of 1 inch : 3.2 m...
 6.6.3.25: USING SIMILAR TRIANGLES In the diagram, nABC , nDEF. D FEB19 4510 2...
 6.6.4.25: MULTISTEP PROBLEM In the diagram, ] AB i ] DC , AE 5 6, AB 5 8, CE...
 6.6.5.25: CHALLENGE In the figure at the right, nABC , nVWX. 45 Y WBA12 D CV5...
 6.6.1.25: ALGEBRA Solve the proportion. 2}7 5 12}z
 6.6.6.25: SHORT RESPONSE Sketch an isosceles triangle. Draw a ray that bisect...
 6.6.7.26: POTTERY Your pottery is used on a poster for a student art show. Yo...
 6.6.2.26: MAP READING The map of a hiking trail has a scale of 1 inch : 3.2 m...
 6.6.3.26: USING SIMILAR TRIANGLES In the diagram, nABC , nDEF. D FEB19 4510 2...
 6.6.4.26: REASONING In Exercises 2629, is it possible for nJKL and nXYZ to be...
 6.6.5.26: CHALLENGE In the figure at the right, nABC , nVWX. 45 Y WBA12 D CV5...
 6.6.1.26: ALGEBRA Solve the proportion. j 1 1 }5 5 4}10
 6.6.6.26: PLAN FOR PROOF Use the diagram given for the proof of Theorem 6.4 i...
 6.6.7.27: SHADOWS You and your friend are walking at night. You point a flash...
 6.6.2.27: POLLEN The photograph shows a particle of goldenrod pollen that has...
 6.6.3.27: SHORT RESPONSE Suppose you are told that nPQR , nXYZ and that the e...
 6.6.4.27: REASONING In Exercises 2629, is it possible for nJKL and nXYZ to be...
 6.6.5.27: CHALLENGE In the figure at the right, nABC , nVWX. 45 Y WBA12 D CV5...
 6.6.1.27: ALGEBRA Solve the proportion. 1c 1 5 5 3}24
 6.6.6.27: PROVING THEOREM 6.7 Use the diagram with the auxiliary lines drawn ...
 6.6.7.28: OPENENDED MATH Describe how you can use dilations to create the fi...
 6.6.2.28: RAMP DESIGN Assume that the wheelchair ramps described each have a ...
 6.6.3.28: MULTIPLE CHOICE The lengths of the legs of right triangle ABC are 3...
 6.6.4.28: REASONING In Exercises 2629, is it possible for nJKL and nXYZ to be...
 6.6.5.28: RACECAR NET Which postulate or theorem could you use to show that t...
 6.6.1.28: ALGEBRA Solve the proportion. 4a 2 3 5 2}5
 6.6.6.28: EXTENDED RESPONSE In perspective drawing, lines that are parallel i...
 6.6.7.29: MULTISTEP PROBLEM nABC has vertices A(3, 23), B(3, 6), and C(15, 6...
 6.6.2.29: RAMP DESIGN Assume that the wheelchair ramps described each have a ...
 6.6.3.29: CHALLENGE Copy the figure at the right and divide it into two simil...
 6.6.4.29: REASONING In Exercises 2629, is it possible for nJKL and nXYZ to be...
 6.6.5.29: STAINED GLASS Certain sections of stained glass are sold in triangu...
 6.6.1.29: ALGEBRA Solve the proportion. 1}1 3b4 5 5}2
 6.6.6.29: CHALLENGE Prove Cevas Theorem: If P is any point inside nABC, then ...
 6.6.7.30: EXTENDED RESPONSE Look at the coordinate notation for a dilation on...
 6.6.2.30: STATISTICS Researchers asked 4887 people to pick a number between 1...
 6.6.3.30: REASONING Is similarity reflexive? symmetric? transitive? Give exam...
 6.6.4.30: HALLENGE If PT 5 x, PQ 5 3x, and SR 5 8 }3 x, find PS in terms of x...
 6.6.5.30: SHUFFLEBOARD In the portion of the shuffleboard court shown, } BC A...
 6.6.1.30: ALGEBRA Solve the proportion. 32p 1 5 5 1}9p
 6.6.6.30: Perform the following operations. Then simplify. (23) p 7}2 (p. 869)
 6.6.7.31: SHORT RESPONSE Explain how you can use dilations to make a perspect...
 6.6.2.31: ALGEBRA Use algebra to verify the property of proportions. Property 2
 6.6.3.31: TENNIS In table tennis, the table is a rectangle 9 feet long and 5 ...
 6.6.4.31: AIR HOCKEY An air hockey player returns the puck to his opponent by...
 6.6.5.31: SHUFFLEBOARD In the portion of the shuffleboard court shown, } BC A...
 6.6.1.31: GEOMETRIC MEAN Find the geometric mean of the two numbers. 2 and 18
 6.6.6.31: Perform the following operations. Then simplify. 4}3 p 1}2 (p. 869)
 6.6.7.32: MIDPOINTS Let }XY be a dilation of }PQ with scale factor k. Show th...
 6.6.2.32: ALGEBRA Use algebra to verify the property of proportions. Property 3
 6.6.3.32: DIGITAL PROJECTOR You are preparing a computer presentation to be d...
 6.6.4.32: LAKES You can measure the width of the lake using a surveying techn...
 6.6.5.32: OPENENDED MATH Use a diagram to show why there is no SideSideAng...
 6.6.1.32: GEOMETRIC MEAN Find the geometric mean of the two numbers. 4 and 25
 6.6.6.32: Perform the following operations. Then simplify. 511}222(p. 871)
 6.6.7.33: REASONING In Exercise 32, show that }XY i }PQ .
 6.6.2.33: ALGEBRA Use algebra to verify the property of proportions. Property 4
 6.6.3.33: MULTIPLE REPRESENTATIONS Use the similar figures shown. The scale f...
 6.6.4.33: SHORT RESPONSE Explain why all equilateral triangles are similar. I...
 6.6.5.33: MULTISTEP PROBLEM Ruby is standing in her back yard and she decide...
 6.6.1.33: GEOMETRIC MEAN Find the geometric mean of the two numbers. 32 and 8
 6.6.6.33: Perform the following operations. Then simplify. 15}423(p. 871)
 6.6.7.34: CHALLENGE A rectangle has vertices A(0, 0), B(0, 6), C(9, 6), and D...
 6.6.2.34: REASONING Use algebra to explain why the property of proportions is...
 6.6.3.34: MULTISTEP PROBLEM During a total eclipse of the sun, the moon is d...
 6.6.4.34: AERIAL PHOTOGRAPHY Lowlevel aerial photos can be taken using a rem...
 6.6.5.34: EXTENDED RESPONSE Suppose you are given two right triangles with on...
 6.6.1.34: GEOMETRIC MEAN Find the geometric mean of the two numbers. 4 and 16
 6.6.6.34: Describe the translation in words and write the coordinate rule for...
 6.6.7.35: Simplify the expression. (p. 873) (3x 1 2)2 1 (x 2 5)2
 6.6.2.35: REASONING Use algebra to explain why the property of proportions is...
 6.6.3.35: SHORT RESPONSE A rectangular image is enlarged on each side by the ...
 6.6.4.35: PROOF Use the given information to draw a sketch. Then write a proo...
 6.6.5.35: PROOF Given that nABC is a right triangle and D, E, and F are midpo...
 6.6.1.35: GEOMETRIC MEAN Find the geometric mean of the two numbers. 2 and 25
 6.6.6.35: Describe the translation in words and write the coordinate rule for...
 6.6.7.36: Simplify the expression. (p. 873) . 411}2 ab2 1 (b 2 a)2
 6.6.2.36: REASONING Use algebra to explain why the property of proportions is...
 6.6.3.36: SHORT RESPONSE How are the areas of similar rectangles related to t...
 6.6.4.36: PROOF Prove that if an acute angle in one right triangle is congrue...
 6.6.5.36: WRITING Can two triangles have all pairs of corresponding angles in...
 6.6.1.36: GEOMETRIC MEAN Find the geometric mean of the two numbers. 6 and 20
 6.6.6.36: Describe the translation in words and write the coordinate rule for...
 6.6.7.37: Simplify the expression. (p. 873) (a 1 b)2 2 (a 2 b)2
 6.6.2.37: CHALLENGE When fruit is dehydrated, water is removed from the fruit...
 6.6.3.37: EXTENDED RESPONSE The equations of two lines in the coordinate plan...
 6.6.4.37: TECHNOLOGY Use a graphing calculator or computer. a. Draw nABC. Dra...
 6.6.5.37: PROVING THEOREM 6.3 Write a paragraph proof of the SAS Similarity T...
 6.6.1.37: ERROR ANALYSIS A student incorrectly simplified the ratio. Describe...
 6.6.7.38: Find the distance between each pair of points. (p. 15) (0, 5) and (...
 6.6.2.38: Over the weekend, Claudia drove a total of 405 miles, driving twice...
 6.6.3.38: PROVING THEOREM 6.1 Prove the Perimeters of Similar Polygons Theore...
 6.6.4.38: EXTENDED RESPONSE Explain how you could use similar triangles to sh...
 6.6.5.38: CHALLENGE A portion of a water slide in an amusement park is shown....
 6.6.1.38: WRITING RATIOS Let x 5 10, y 5 3, and z 5 8. Write the ratio in sim...
 6.6.7.39: Find the distance between each pair of points. (p. 15) (23, 0) and ...
 6.6.2.39: Identify all pairs of congruent corresponding parts. Then write ano...
 6.6.3.39: CHALLENGE In the diagram, PQRS is a square, and PLMS , LMRQ. Find t...
 6.6.4.39: CORRESPONDING LENGTHS Without using the Corresponding Lengths Prope...
 6.6.5.39: Find the slope of the line that passes through the given points. (p...
 6.6.1.39: WRITING RATIOS Let x 5 10, y 5 3, and z 5 8. Write the ratio in sim...
 6.6.7.40: Find the distance between each pair of points. (p. 15) (22, 24) and...
 6.6.2.40: Identify all pairs of congruent corresponding parts. Then write ano...
 6.6.3.40: Given A(1, 1), B(3, 2), C(2, 4), and D11, 7 }22 , determine whether...
 6.6.4.40: CHALLENGE Prove that if the lengths of two sides of a triangle are ...
 6.6.5.40: Find the slope of the line that passes through the given points. (p...
 6.6.1.40: WRITING RATIOS Let x 5 10, y 5 3, and z 5 8. Write the ratio in sim...
 6.6.7.41: Find the value(s) of the variable(s). Area 5 6 in.2 (p. 49) 3 in.h ...
 6.6.3.41: Given A(1, 1), B(3, 2), C(2, 4), and D11, 7 }22 , determine whether...
 6.6.4.41: In Exercises 4144, use the diagram. 26481 Name three pairs of corre...
 6.6.5.41: Find the slope of the line that passes through the given points. (p...
 6.6.1.41: WRITING RATIOS Let x 5 10, y 5 3, and z 5 8. Write the ratio in sim...
 6.6.7.42: Find the value(s) of the variable(s). n ABC > n DCB (p. 256) Dy 1 7...
 6.6.3.42: Given A(1, 1), B(3, 2), C(2, 4), and D11, 7 }22 , determine whether...
 6.6.4.42: In Exercises 4144, use the diagram. 26481 Name two pairs of alterna...
 6.6.5.42: State the postulate or theorem you would use to prove the triangles...
 6.6.1.42: ALGEBRA Solve the proportion. 2}x 1 53 5 x}2 54
 6.6.7.43: Find the value(s) of the variable(s). n PQR is isosceles. (p. 303) ...
 6.6.3.43: Find the measure of the exterior angle shown. (p. 217) 3. 1(3x 2 50)8x
 6.6.4.43: In Exercises 4144, use the diagram. 26481 Name two pairs of alterna...
 6.6.5.43: Find the value of x. DE is a midsegment of nABC. (p. 295) A E CDB15
 6.6.1.43: ALGEBRA Solve the proportion. 2}2 s3 5 2}s 1 15
 6.6.3.44: Find the measure of the exterior angle shown. (p. 218) (2x 1 20)840...
 6.6.4.44: In Exercises 4144, use the diagram. 26481 Find m 1 1 m 7. (p. 154)
 6.6.5.44: Find the value of x. GKGH 5 JK}FH (p. 364) F x HJ KG
 6.6.1.44: ALGEBRA Solve the proportion. 15}m 5 m}5
 6.6.3.45: Find the measure of the exterior angle shown. (p. 219) (3x 1 8)8[6(...
 6.6.4.45: CONGRUENCE Explain why nABE > nCDE. (p. 240) AED
 6.6.1.45: ALGEBRA Solve the proportion. 7q 1 1 5 q}2 15
 6.6.3.46: Copy and complete the statement with <, >, or 5. (p. 335) RS ? TU 1...
 6.6.4.46: Simplify the ratio. (p. 356) 4}20
 6.6.1.46: ANGLE MEASURES The ratio of the measures of two supplementary angle...
 6.6.3.47: Copy and complete the statement with <, >, or 5. (p. 335) FG ? HD H...
 6.6.4.47: Simplify the ratio. (p. 356) 36}18
 6.6.1.47: SHORT RESPONSE The ratio of the measure of an exterior angle of a t...
 6.6.3.48: Copy and complete the statement with <, >, or 5. (p. 335) WX ? YX W...
 6.6.4.48: Simplify the ratio. (p. 356) 21 : 63
 6.6.1.48: SHORT RESPONSE Without knowing its side lengths, can you determine ...
 6.6.4.49: Simplify the ratio. (p. 356) 42 : 28
 6.6.1.49: ALGEBRA In Exercises 4951, the ratio of two side lengths for the tr...
 6.6.1.50: ALGEBRA In Exercises 4951, the ratio of two side lengths for the tr...
 6.6.1.51: ALGEBRA In Exercises 4951, the ratio of two side lengths for the tr...
 6.6.1.52: MULTIPLE CHOICE What is a value of x that makes x }3 5} 4x x 1 3 tr...
 6.6.1.53: AREA The area of a rectangle is 4320 square inches. The ratio of th...
 6.6.1.54: COORDINATE GEOMETRY The points (23, 2), (1, 1), and (x, 0) are coll...
 6.6.1.55: ALGEBRA Use the proportions } a 1 b 2a 2 b 5 5 }4 and} b a 1 9 5 5 ...
 6.6.1.56: CHALLENGE Find the ratio of x to y given that 5 }y 1 7 }x 5 24 and ...
 6.6.1.57: TILING The perimeter of a room is 66 feet. The ratio of its length ...
 6.6.1.58: GEARS The gear ratio of two gears is the ratio of the number of tee...
 6.6.1.59: TRAIL MIX You need to make 36 onehalf cup bags of trail mix for a ...
 6.6.1.60: PAPER SIZES International standard paper sizes are commonly used al...
 6.6.1.61: BATTING AVERAGE The batting average of a baseball player is the rat...
 6.6.1.62: MULTISTEP PROBLEM The population of Redtailed hawks is increasing...
 6.6.1.63: SHORT RESPONSE Some common computer screen resolutions are 1024 : 7...
 6.6.1.64: BIOLOGY The larvae of the MotherofPearl moth is the fastest movin...
 6.6.1.65: CURRENCY EXCHANGE Emily took 500 U.S. dollars to the bank to exchan...
 6.6.1.66: MULTIPLE REPRESENTATIONS Let x and y be two positive numbers whose ...
 6.6.1.67: ALGEBRA Use algebra to verify Property 1, the Cross Products Property.
 6.6.1.68: ALGEBRA Show that the geometric mean of two numbers is equal to the...
 6.6.1.69: CHALLENGE In Exercises 6971, use the given information to find the ...
 6.6.1.70: CHALLENGE In Exercises 6971, use the given information to find the ...
 6.6.1.71: CHALLENGE In Exercises 6971, use the given information to find the ...
 6.6.1.72: Find the reciprocal. (p. 869) 26
 6.6.1.73: Find the reciprocal. (p. 869) 1}13
 6.6.1.74: Find the reciprocal. (p. 869) 2363
 6.6.1.75: Find the reciprocal. (p. 869) 20.2
 6.6.1.76: Solve the quadratic equation. (p. 882) 5x2 5 35
 6.6.1.77: Solve the quadratic equation. (p. 882) x2 2 20 5 29
 6.6.1.78: Solve the quadratic equation. (p. 882) (x 2 3)(x 1 3) 5 27
 6.6.1.79: Write the equation of the line with the given description. (p. 180)...
 6.6.1.80: Write the equation of the line with the given description. (p. 180)...
Solutions for Chapter 6: Ratios, Proportions, and the Geometric Mean
Full solutions for Geometry (Holt McDougal Larson Geometry)  1st Edition
ISBN: 9780618595402
Solutions for Chapter 6: Ratios, Proportions, and the Geometric Mean
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 6: Ratios, Proportions, and the Geometric Mean includes 361 full stepbystep solutions. This textbook survival guide was created for the textbook: Geometry (Holt McDougal Larson Geometry), edition: 1. Since 361 problems in chapter 6: Ratios, Proportions, and the Geometric Mean have been answered, more than 26693 students have viewed full stepbystep solutions from this chapter. Geometry (Holt McDougal Larson Geometry) was written by and is associated to the ISBN: 9780618595402.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Outer product uv T
= column times row = rank one matrix.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B IIĀ·

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.