 8.8.3.1: VOCABULARY Explain how knowing that }AB i }CD and }AD i }BC allows ...
 8.8.4.1: VOCABULARY What is another name for an equilateral rectangle?
 8.8.5.1: VOCABULARY In trapezoid PQRS, }PQ i }RS . Sketch PQRS and identify ...
 8.8.1.1: VOCABULARY Sketch a convex hexagon. Draw all of its diagonals.
 8.8.6.1: VOCABULARY Copy and complete: A quadrilateral that has exactly one ...
 8.8.2.1: VOCABULARY What property of a parallelogram is included in the defi...
 8.1: In Exercises 1 and 2, copy and complete the statement. The ? of a t...
 8.8.3.2: WRITING A quadrilateral has four congruent sides. Is the quadrilate...
 8.8.4.2: WRITING Do you have enough information to identify the figure at th...
 8.8.5.2: WRITING Describe the differences between a kite and a trapezoid.
 8.8.1.2: WRITING How many exterior angles are there in an ngon? Are all the...
 8.8.6.2: WRITING Describe three methods you could use to prove that a parall...
 8.8.2.2: WRITING In parallelogram ABCD, m A 5 658. Explain how you would fin...
 8.2: In Exercises 1 and 2, copy and complete the statement. A(n) ? of a ...
 8.8.3.3: ERROR ANALYSIS A student claims that because two pairs of sides are...
 8.8.4.3: RHOMBUSES For any rhombus JKLM, decide whether the statement is alw...
 8.8.5.3: COORDINATE PLANE Points A, B, C, and D are the vertices of a quadri...
 8.8.1.3: INTERIOR ANGLE SUMS Find the sum of the measures of the interior an...
 8.8.6.3: PROPERTIES OF QUADRILATERALS Copy the chart. Put an X in the box if...
 8.8.2.3: ALGEBRA Find the value of each variable in the parallelogram. 59yx
 8.3: WRITING Describe the different ways you can show that a trapezoid i...
 8.8.3.4: REASONING What theorem can you use to show that the quadrilateral i...
 8.8.4.4: RHOMBUSES For any rhombus JKLM, decide whether the statement is alw...
 8.8.5.4: COORDINATE PLANE Points A, B, C, and D are the vertices of a quadri...
 8.8.1.4: INTERIOR ANGLE SUMS Find the sum of the measures of the interior an...
 8.8.6.4: PROPERTIES OF QUADRILATERALS Copy the chart. Put an X in the box if...
 8.8.2.4: ALGEBRA Find the value of each variable in the parallelogram. 2nm
 8.4: In Exercises 46, match the figure with the most specific name. A. S...
 8.8.3.5: REASONING What theorem can you use to show that the quadrilateral i...
 8.8.4.5: RHOMBUSES For any rhombus JKLM, decide whether the statement is alw...
 8.8.5.5: COORDINATE PLANE Points A, B, C, and D are the vertices of a quadri...
 8.8.1.5: INTERIOR ANGLE SUMS Find the sum of the measures of the interior an...
 8.8.6.5: PROPERTIES OF QUADRILATERALS Copy the chart. Put an X in the box if...
 8.8.2.5: ALGEBRA Find the value of each variable in the parallelogram. 558a8
 8.5: In Exercises 46, match the figure with the most specific name. B. P...
 8.8.3.6: REASONING What theorem can you use to show that the quadrilateral i...
 8.8.4.6: RHOMBUSES For any rhombus JKLM, decide whether the statement is alw...
 8.8.5.6: COORDINATE PLANE Points A, B, C, and D are the vertices of a quadri...
 8.8.1.6: INTERIOR ANGLE SUMS Find the sum of the measures of the interior an...
 8.8.6.6: PROPERTIES OF QUADRILATERALS Copy the chart. Put an X in the box if...
 8.8.2.6: ALGEBRA Find the value of each variable in the parallelogram. 2p81208
 8.6: In Exercises 46, match the figure with the most specific name. C. R...
 8.8.3.7: SHORT RESPONSE When you shift gears on a bicycle, a mechanism calle...
 8.8.4.7: RHOMBUSES For any rhombus JKLM, decide whether the statement is alw...
 8.8.5.7: FINDING ANGLE MEASURES Find m J, m L, and m M. K L 508
 8.8.1.7: FINDING NUMBER OF SIDES The sum of the measures of the interior ang...
 8.8.6.7: PROPERTIES OF QUADRILATERALS Copy the chart. Put an X in the box if...
 8.8.2.7: ALGEBRA Find the value of each variable in the parallelogram. d 2 2...
 8.7: The sum of the measures of the interior angles of a convex regular ...
 8.8.3.8: ALGEBRA For what value of x is the quadrilateral a parallelogram? 2...
 8.8.4.8: RHOMBUSES For any rhombus JKLM, decide whether the statement is alw...
 8.8.5.8: FINDING ANGLE MEASURES Find m J, m L, and m M. JLK1008
 8.8.1.8: FINDING NUMBER OF SIDES The sum of the measures of the interior ang...
 8.8.6.8: PROPERTIES OF QUADRILATERALS Copy the chart. Put an X in the box if...
 8.8.2.8: ALGEBRA Find the value of each variable in the parallelogram. (g 1 4)8
 8.8: In Exercises 810, find the value of x. 1208x89781308150
 8.8.3.9: ALGEBRA For what value of x is the quadrilateral a parallelogram? 4...
 8.8.4.9: RECTANGLES For any rectangle WXYZ, decide whether the statement is ...
 8.8.5.9: FINDING ANGLE MEASURES Find m J, m L, and m M. K 1188
 8.8.1.9: FINDING NUMBER OF SIDES The sum of the measures of the interior ang...
 8.8.6.9: PROPERTIES OF QUADRILATERALS Copy the chart. Put an X in the box if...
 8.8.2.9: FINDING ANGLE MEASURES Find the measure of the indicated angle in t...
 8.9: In Exercises 810, find the value of x. x82x8 125811081478 1128
 8.8.3.10: ALGEBRA For what value of x is the quadrilateral a parallelogram? 6...
 8.8.4.10: RECTANGLES For any rectangle WXYZ, decide whether the statement is ...
 8.8.5.10: REASONING Determine whether the quadrilateral is a trapezoid. Expla...
 8.8.1.10: FINDING NUMBER OF SIDES The sum of the measures of the interior ang...
 8.8.6.10: PROPERTIES OF QUADRILATERALS Copy the chart. Put an X in the box if...
 8.8.2.10: FINDING ANGLE MEASURES Find the measure of the indicated angle in t...
 8.10: In Exercises 810, find the value of x. 5x85x88x
 8.8.3.11: COORDINATE GEOMETRY The vertices of quadrilateral ABCD are given. D...
 8.8.4.11: RECTANGLES For any rectangle WXYZ, decide whether the statement is ...
 8.8.5.11: REASONING Determine whether the quadrilateral is a trapezoid. Expla...
 8.8.1.11: ALGEBRA Find the value of x. 86814081388
 8.8.6.11: PROPERTIES OF QUADRILATERALS Copy the chart. Put an X in the box if...
 8.8.2.11: FINDING ANGLE MEASURES Find the measure of the indicated angle in t...
 8.11: In a regular nonagon, the exterior angles are all congruent. What i...
 8.8.3.12: COORDINATE GEOMETRY The vertices of quadrilateral ABCD are given. D...
 8.8.4.12: RECTANGLES For any rectangle WXYZ, decide whether the statement is ...
 8.8.5.12: REASONING Determine whether the quadrilateral is a trapezoid. Expla...
 8.8.1.12: ALGEBRA Find the value of x. x816281218 9681018
 8.8.6.12: ERROR ANALYSIS Describe and correct the error in classifying the qu...
 8.8.2.12: SKETCHING In ~PQRS, m R is 24 degrees more than m S. Sketch ~PQRS. ...
 8.12: Find the value of each variable in the parallelogram. 108n 2 3m
 8.8.3.13: COORDINATE GEOMETRY The vertices of quadrilateral ABCD are given. D...
 8.8.4.13: RECTANGLES For any rectangle WXYZ, decide whether the statement is ...
 8.8.5.13: FINDING MIDSEGMENTS Find the length of the midsegment of the trapez...
 8.8.1.13: ALGEBRA Find the value of x. x82x8 14381398152811681258140
 8.8.6.13: MULTIPLE CHOICE What is the most specific name for the quadrilatera...
 8.8.2.13: ALGEBRA Find the value of each variable in the parallelogram. 15 95a
 8.13: Find the value of each variable in the parallelogram. 11 14c 1 5d 1 4
 8.8.3.14: COORDINATE GEOMETRY The vertices of quadrilateral ABCD are given. D...
 8.8.4.14: RECTANGLES For any rectangle WXYZ, decide whether the statement is ...
 8.8.5.14: FINDING MIDSEGMENTS Find the length of the midsegment of the trapez...
 8.8.1.14: ALGEBRA Find the value of x. x87886581068
 8.8.6.14: CLASSIFYING QUADRILATERALS Give the most specific name for the quad...
 8.8.2.14: ALGEBRA Find the value of each variable in the parallelogram. 16 2n...
 8.14: Find the value of each variable in the parallelogram. 18a 2 10(b 1 ...
 8.8.3.15: REASONING Describe how to prove that ABCD is a parallelogram. BD C
 8.8.4.15: CLASSIFYING Classify the quadrilateral. Explain your reasoning.
 8.8.5.15: FINDING MIDSEGMENTS Find the length of the midsegment of the trapez...
 8.8.1.15: ALGEBRA Find the value of x. 2x8x8 45
 8.8.6.15: CLASSIFYING QUADRILATERALS Give the most specific name for the quad...
 8.8.2.15: ALGEBRA Find the value of each variable in the parallelogram. 5y 12...
 8.15: In ~PQRS, PQ 5 5 centimeters, QR 5 10 centimeters, and m PQR 5 368....
 8.8.3.16: REASONING Describe how to prove that ABCD is a parallelogram. A BD C
 8.8.4.16: CLASSIFYING Classify the quadrilateral. Explain your reasoning.
 8.8.5.16: MULTIPLE CHOICE Which statement is not always true? A The base angl...
 8.8.1.16: ALGEBRA Find the value of x. 508398588488598
 8.8.6.16: CLASSIFYING QUADRILATERALS Give the most specific name for the quad...
 8.8.2.16: MULTIPLE CHOICE The diagonals of parallelogram OPQR intersect at po...
 8.16: The perimeter of ~EFGH is 16 inches. If EF is 5 inches, find the le...
 8.8.3.17: REASONING Describe how to prove that ABCD is a parallelogram. A BD C
 8.8.4.17: CLASSIFYING Classify the quadrilateral. Explain your reasoning. 140...
 8.8.5.17: ERROR ANALYSIS Describe and correct the error made in finding m A. ...
 8.8.1.17: ERROR ANALYSIS A student claims that the sum of the measures of the...
 8.8.6.17: DRAWING Draw a quadrilateral with congruent diagonals and exactly o...
 8.8.2.17: REASONING Use the photo to copy and complete the statement. Explain...
 8.17: In ~JKLM, the ratio of the measure of J to the measure of M is 5 : ...
 8.8.3.18: MULTIPLE CHOICE In quadrilateral WXYZ,}WZ and }XY are congruent and...
 8.8.4.18: USING PROPERTIES Sketch rhombus STUV. Describe everything you know ...
 8.8.5.18: ANGLES OF KITES EFGH is a kite. Find m G. EGH 1008 408
 8.8.1.18: MULTIPLE CHOICE The measures of the interior angles of a quadrilate...
 8.8.6.18: IDENTIFYING QUADRILATERALS Tell whether enough information is given...
 8.8.2.18: REASONING Use the photo to copy and complete the statement. Explain...
 8.18: For what value of x is the quadrilateral a parallelogram? 2x 1 4x 1 9
 8.8.3.19: ALGEBRA For what value of x is the quadrilateral a parallelogram? 6...
 8.8.4.19: USING PROPERTIES Name each quadrilateralparallelogram, rectangle, r...
 8.8.5.19: ANGLES OF KITES EFGH is a kite. Find m G. E 6081108
 8.8.1.19: REGULAR POLYGONS Find the measures of an interior angle and an exte...
 8.8.6.19: IDENTIFYING QUADRILATERALS Tell whether enough information is given...
 8.8.2.19: REASONING Use the photo to copy and complete the statement. Explain...
 8.19: For what value of x is the quadrilateral a parallelogram? 3x 1 25x 2 4
 8.8.3.20: ALGEBRA For what value of x is the quadrilateral a parallelogram? x...
 8.8.4.20: USING PROPERTIES Name each quadrilateralparallelogram, rectangle, r...
 8.8.5.20: ANGLES OF KITES EFGH is a kite. Find m G. HE 1508
 8.8.1.20: REGULAR POLYGONS Find the measures of an interior angle and an exte...
 8.8.6.20: IDENTIFYING QUADRILATERALS Tell whether enough information is given...
 8.8.2.20: REASONING Use the photo to copy and complete the statement. Explain...
 8.20: Classify the special quadrilateral. Then find the values of x and y...
 8.8.3.21: ALGEBRA For what value of x is the quadrilateral a parallelogram? x...
 8.8.4.21: USING PROPERTIES Name each quadrilateralparallelogram, rectangle, r...
 8.8.5.21: DIAGONALS OF KITES Use Theorem 8.18 and the Pythagorean Theorem to ...
 8.8.1.21: REGULAR POLYGONS Find the measures of an interior angle and an exte...
 8.8.6.21: COORDINATE PLANE Points P, Q, R, and S are the vertices of a quadri...
 8.8.2.21: REASONING Use the photo to copy and complete the statement. Explain...
 8.21: Classify the special quadrilateral. Then find the values of x and y...
 8.8.3.22: BICONDITIONALS Write the indicated theorems as a biconditional stat...
 8.8.4.22: USING PROPERTIES Name each quadrilateralparallelogram, rectangle, r...
 8.8.5.22: DIAGONALS OF KITES Use Theorem 8.18 and the Pythagorean Theorem to ...
 8.8.1.22: DIAGONALS OF SIMILAR FIGURES Hexagons RSTUVW and JKLMNP are similar...
 8.8.6.22: COORDINATE PLANE Points P, Q, R, and S are the vertices of a quadri...
 8.8.2.22: REASONING Use the photo to copy and complete the statement. Explain...
 8.22: The diagonals of a rhombus are 10 centimeters and 24 centimeters. F...
 8.8.3.23: BICONDITIONALS Write the indicated theorems as a biconditional stat...
 8.8.4.23: USING PROPERTIES Name each quadrilateralparallelogram, rectangle, r...
 8.8.5.23: DIAGONALS OF KITES Use Theorem 8.18 and the Pythagorean Theorem to ...
 8.8.1.23: SHORT RESPONSE Explain why any two regular pentagons are similar.
 8.8.6.23: COORDINATE PLANE Points P, Q, R, and S are the vertices of a quadri...
 8.8.2.23: USING A DIAGRAM Find the indicated measure in ~EFGH. Explain. E F45...
 8.23: In Exercises 23 and 24, use the diagram of a recycling container. O...
 8.8.3.24: REASONING Follow the steps below to draw a parallelogram. Explain w...
 8.8.4.24: USING PROPERTIES Name each quadrilateralparallelogram, rectangle, r...
 8.8.5.24: ERROR ANALYSIS In trapezoid ABCD, MN}is the midsegment. Describe an...
 8.8.1.24: REGULAR POLYGONS Find the value of n for each regular ngon describ...
 8.8.6.24: COORDINATE PLANE Points P, Q, R, and S are the vertices of a quadri...
 8.8.2.24: USING A DIAGRAM Find the indicated measure in ~EFGH. Explain. E F45...
 8.24: In Exercises 23 and 24, use the diagram of a recycling container. O...
 8.8.3.25: COORDINATE GEOMETRY Three of the vertices of ~ABCD are given. Find ...
 8.8.4.25: ERROR ANALYSIS Quadrilateral PQRS is a rectangle. Describe and corr...
 8.8.5.25: ALGEBRA Find the value of x. 1072x
 8.8.1.25: REGULAR POLYGONS Find the value of n for each regular ngon describ...
 8.8.6.25: TECHNOLOGY Use geometry drawing software to draw points A, B, C, an...
 8.8.2.25: USING A DIAGRAM Find the indicated measure in ~EFGH. Explain. E F45...
 8.25: Give the most specific name for the quadrilateral. Explain your rea...
 8.8.3.26: COORDINATE GEOMETRY Three of the vertices of ~ABCD are given. Find ...
 8.8.4.26: ALGEBRA Classify the special quadrilateral. Explain your reasoning....
 8.8.5.26: ALGEBRA Find the value of x. 3x 1 112.515
 8.8.1.26: POSSIBLE POLYGONS Determine if it is possible for a regular polygon...
 8.8.6.26: DEVELOPING PROOF Which pairs of segments or angles must be congruen...
 8.8.2.26: USING A DIAGRAM Find the indicated measure in ~EFGH. Explain. E F45...
 8.26: Give the most specific name for the quadrilateral. Explain your rea...
 8.8.3.27: COORDINATE GEOMETRY Three of the vertices of ~ABCD are given. Find ...
 8.8.4.27: ALGEBRA Classify the special quadrilateral. Explain your reasoning....
 8.8.5.27: ALGEBRA Find the value of x. 5x18.712x 2 1.7
 8.8.1.27: CHALLENGE Sides are added to a convex polygon so that the sum of it...
 8.8.6.27: DEVELOPING PROOF Which pairs of segments or angles must be congruen...
 8.8.2.27: USING A DIAGRAM Find the indicated measure in ~EFGH. Explain. E F45...
 8.27: Give the most specific name for the quadrilateral. Explain your rea...
 8.8.3.28: COORDINATE GEOMETRY Three of the vertices of ~ABCD are given. Find ...
 8.8.4.28: ALGEBRA Classify the special quadrilateral. Explain your reasoning....
 8.8.5.28: SHORT RESPONSE The points M(23, 5), N(21, 5), P(3, 21), and Q(25, 2...
 8.8.1.28: BASEBALL The outline of the playing field at a baseball park is a p...
 8.8.6.28: DEVELOPING PROOF Which pairs of segments or angles must be congruen...
 8.8.2.28: USING A DIAGRAM Find the indicated measure in ~EFGH. Explain. E F45...
 8.28: In quadrilateral RSTU, R, T, and U are right angles, and RS 5 ST. W...
 8.8.3.29: CONSTRUCTION There is more than one way to use a compass and a stra...
 8.8.4.29: ALGEBRA Classify the special quadrilateral. Explain your reasoning....
 8.8.5.29: DRAWING In trapezoid JKLM, }JK i}LM and JK 5 17. The midsegment of ...
 8.8.1.29: BASEBALL The outline of the playing field at a baseball park is a p...
 8.8.6.29: TRAPEZOIDS In Exercises 2931, determine whether there is enough inf...
 8.8.2.29: MULTIPLE CHOICE In parallelogram ABCD, AB 5 14 inches and BC 5 20 i...
 8.8.3.30: CHALLENGE In the diagram, ABCD is a parallelogram, BF 5 DE 5 12, an...
 8.8.4.30: SHORT RESPONSE The diagonals of a rhombus are 6 inches and 8 inches...
 8.8.5.30: RATIOS The ratio of the lengths of the bases of a trapezoid is 1 : ...
 8.8.1.30: JEWELRY BOX The base of a jewelry box is shaped like a regular hexa...
 8.8.6.30: TRAPEZOIDS In Exercises 2931, determine whether there is enough inf...
 8.8.2.30: ALGEBRA The measure of one interior angle of a parallelogram is 0.2...
 8.8.3.31: AUTOMOBILE REPAIR The diagram shows an automobile lift. A bus drive...
 8.8.4.31: MULTIPLE CHOICE Rectangle ABCD is similar to rectangle FGHJ. If AC ...
 8.8.5.31: MULTIPLE CHOICE In trapezoid PQRS, }PQ i }RS and}MN is the midsegme...
 8.8.1.31: GREENHOUSE The floor of the greenhouse shown is a shaped like a reg...
 8.8.6.31: TRAPEZOIDS In Exercises 2931, determine whether there is enough inf...
 8.8.2.31: ALGEBRA The measure of one interior angle of a parallelogram is 50 ...
 8.8.3.32: MUSIC STAND A music stand can be folded up, as shown below. In the ...
 8.8.4.32: RHOMBUS The diagonals of rhombus ABCD intersect at E. Given that m ...
 8.8.5.32: CHALLENGE The figure shown at the right is a trapezoid with its mid...
 8.8.1.32: MULTISTEP PROBLEM In pentagon PQRST, P, Q, and S are right angles,...
 8.8.6.32: CHALLENGE Draw a rectangle and bisect its angles. What type of quad...
 8.8.2.32: ERROR ANALYSIS In ~ABCD, m B 5 508. A student says that m A 5 508. ...
 8.8.3.33: PROVING THEOREM 8.9 Use the diagram of PQRS with the auxiliary line...
 8.8.4.33: RHOMBUS The diagonals of rhombus ABCD intersect at E. Given that m ...
 8.8.5.33: REASONING Explain why a kite and a general quadrilateral are the on...
 8.8.1.33: PROVING THEOREM 8.1 FOR PENTAGONS The Polygon Interior Angles Theor...
 8.8.6.33: REALWORLD OBJECTS What type of special quadrilateral is outlined?
 8.8.2.33: USING A DIAGRAM In the diagram, QRST and STUV are parallelograms. F...
 8.8.3.34: REASONING A student claims incorrectly that the marked information ...
 8.8.4.34: RHOMBUS The diagonals of rhombus ABCD intersect at E. Given that m ...
 8.8.5.34: FURNITURE In the photograph of a chest of drawers,}HC is the midseg...
 8.8.1.34: PROVING A COROLLARY Write a paragraph proof of the Corollary to the...
 8.8.6.34: REALWORLD OBJECTS What type of special quadrilateral is outlined? ...
 8.8.2.34: FINDING A PERIMETER The sides of ~MNPQ are represented by the expre...
 8.8.3.35: REASONING A student claims incorrectly that the marked information ...
 8.8.4.35: RHOMBUS The diagonals of rhombus ABCD intersect at E. Given that m ...
 8.8.5.35: GRAPHIC DESIGN You design a logo in the shape of a convex kite. The...
 8.8.1.35: PROVING THEOREM 8.2 Use the plan below to write a paragraph proof o...
 8.8.6.35: REALWORLD OBJECTS What type of special quadrilateral is outlined?
 8.8.2.35: SHORT RESPONSE In ABCD, m B 5 1248, m A 5 668, and m C 5 1248. Expl...
 8.8.3.36: REASONING A student claims incorrectly that the marked information ...
 8.8.4.36: RHOMBUS The diagonals of rhombus ABCD intersect at E. Given that m ...
 8.8.5.36: EXTENDED RESPONSE The bridge below is designed to fold up into an o...
 8.8.1.36: MULTIPLE REPRESENTATIONS The formula for the measure of each interi...
 8.8.6.36: PYRAMID Use the photo of the Pyramid of Kukulcan in Mexico. a. EF}i...
 8.8.2.36: FINDING ANGLE MEASURES In ~LMNP shown at the right, m MLN 5 328, m ...
 8.8.3.37: EXTENDED RESPONSE Theorem 8.5 states that if a quadrilateral is a p...
 8.8.4.37: RHOMBUS The diagonals of rhombus ABCD intersect at E. Given that m ...
 8.8.5.37: PROVING THEOREM 8.14 Use the diagram and the auxiliary segment to p...
 8.8.1.37: EXTENDED RESPONSE In a concave polygon, at least one interior angle...
 8.8.6.37: SHORT RESPONSE Explain why a parallelogram with one right angle mus...
 8.8.2.37: CHALLENGE Points A(1, 2), B(3, 6), and C(6, 4) are three vertices o...
 8.8.3.38: PROVING THEOREM 8.8 Prove Theorem 8.8. GIVEN c A > C, B > D PROVE c...
 8.8.4.38: RECTANGLE The diagonals of rectangle QRST intersect at P. Given tha...
 8.8.5.38: PROVING THEOREM 8.15 Use the diagram and the auxiliary segment to p...
 8.8.1.38: CHALLENGE Polygon ABCDEFGH is a regular octagon. Suppose sides AB}a...
 8.8.6.38: EXTENDED RESPONSE Segments AC and BD bisect each other. a. Suppose ...
 8.8.2.38: AIRPLANE The diagram shows the mechanism for opening the canopy on ...
 8.8.3.39: PROVING THEOREM 8.10 Prove Theorem 8.10. GIVEN c Diagonals }JL and}...
 8.8.4.39: RECTANGLE The diagonals of rectangle QRST intersect at P. Given tha...
 8.8.5.39: PROVING THEOREM 8.16 Prove part of Theorem 8.16. GIVEN c JKLM is an...
 8.8.1.39: Find m 1 and m 2. Explain your reasoning. (p. 154) 1988 2
 8.8.6.39: MULTISTEP PROBLEM Polygon QRSTUV shown at the right is a regular h...
 8.8.2.39: MIRROR The mirror shown is attached to the wall by an arm that can ...
 8.8.3.40: PROOF Use the diagram at the right. GIVEN c DEBF is a parallelogram...
 8.8.4.40: RECTANGLE The diagonals of rectangle QRST intersect at P. Given tha...
 8.8.5.40: REASONING In the diagram below, }BG is the midsegment of nACD and }...
 8.8.1.40: Find m 1 and m 2. Explain your reasoning. (p. 154) 215
 8.8.6.40: REASONING In quadrilateral WXYZ,}WY and }XZ intersect each other at...
 8.8.2.40: USING RATIOS In ~LMNO, the ratio of LM to MN is 4 : 3. Find LM if t...
 8.8.3.41: REASONING In the diagram, the midpoints of the sides of a quadrilat...
 8.8.4.41: RECTANGLE The diagonals of rectangle QRST intersect at P. Given tha...
 8.8.5.41: PROVING THEOREM 8.18 Prove Theorem 8.18. GIVEN c ABCD is a kite. }A...
 8.8.1.41: Find m 1 and m 2. Explain your reasoning. (p. 154) 121268
 8.8.6.41: CHALLENGE What special type of quadrilateral is EFGH? Write a parag...
 8.8.2.41: OPENENDED MATH Draw a triangle. Copy the triangle and combine the ...
 8.8.3.42: CHALLENGE Show that if ABCD is a parallelogram with its diagonals i...
 8.8.4.42: RECTANGLE The diagonals of rectangle QRST intersect at P. Given tha...
 8.8.5.42: PROVING THEOREM 8.19 Write a paragraph proof of Theorem 8.19. GIVEN...
 8.8.1.42: Quadrilaterals JKLM and PQRS are similar. If JK 5 3.6 centimeters a...
 8.8.6.42: CHALLENGE What special type of quadrilateral is EFGH? Write a parag...
 8.8.2.42: PROVING THEOREM 8.4 Use the diagram of quadrilateral ABCD with the ...
 8.8.3.43: In Exercises 4345, draw a figure that fits the description. (p. 42)...
 8.8.4.43: RECTANGLE The diagonals of rectangle QRST intersect at P. Given tha...
 8.8.5.43: CHALLENGE In Exercise 39, you proved that part of Theorem 8.16 is t...
 8.8.1.43: Quadrilaterals ABCD and EFGH are similar. The scale factor of ABCD ...
 8.8.6.43: In Exercises 43 and 44, use the diagram. (p. 264) By x 1 37 Find th...
 8.8.2.43: PROVING THEOREM 8.5 Use properties of parallel lines to prove Theor...
 8.8.3.44: In Exercises 4345, draw a figure that fits the description. (p. 42)...
 8.8.4.44: SQUARE The diagonals of square LMNP intersect at K. Given that LK 5...
 8.8.5.44: Place a right triangle in a coordinate plane in a way that is conve...
 8.8.1.44: Let A be an acute angle in a right triangle. Approximate the measur...
 8.8.6.44: In Exercises 43 and 44, use the diagram. (p. 264) By x 1 37 Find m ...
 8.8.2.44: PROVING THEOREM 8.6 Theorem 8.6 states that if a quadrilateral is a...
 8.8.3.45: In Exercises 4345, draw a figure that fits the description. (p. 42)...
 8.8.4.45: SQUARE The diagonals of square LMNP intersect at K. Given that LK 5...
 8.8.5.45: Use the diagram to complete the proportion. (p. 449) B CDA ABAC 5 }?AB
 8.8.1.45: Let A be an acute angle in a right triangle. Approximate the measur...
 8.8.6.45: The vertices of quadrilateral ABCD are A(22, 1), B(2, 5), C(3, 2), ...
 8.8.2.45: CHALLENGE Suppose you choose a point on the base of an isosceles tr...
 8.8.3.46: The width of a rectangle is 4 centimeters less than its length. The...
 8.8.4.46: SQUARE The diagonals of square LMNP intersect at K. Given that LK 5...
 8.8.5.46: Use the diagram to complete the proportion. (p. 449) B CDA ABBC 5 }BD?
 8.8.1.46: Let A be an acute angle in a right triangle. Approximate the measur...
 8.8.6.46: The vertices of quadrilateral ABCD are A(22, 1), B(2, 5), C(3, 2), ...
 8.8.2.46: Tell whether the lines through the given points are parallel, perpe...
 8.8.3.47: Find the values of x and y in the triangle shown at the right. Writ...
 8.8.4.47: SQUARE The diagonals of square LMNP intersect at K. Given that LK 5...
 8.8.5.47: Three of the vertices of ~ABCD are given. Find the coordinates of p...
 8.8.1.47: Let A be an acute angle in a right triangle. Approximate the measur...
 8.8.6.47: Use the diagram of ~WXYZ to find the indicated length. (p. 515) V 4...
 8.8.2.47: Tell whether the lines through the given points are parallel, perpe...
 8.8.4.48: SQUARE The diagonals of square LMNP intersect at K. Given that LK 5...
 8.8.5.48: Three of the vertices of ~ABCD are given. Find the coordinates of p...
 8.8.6.48: Use the diagram of ~WXYZ to find the indicated length. (p. 515) V 4...
 8.8.2.48: Tell whether the lines through the given points are parallel, perpe...
 8.8.4.49: SQUARE The diagonals of square LMNP intersect at K. Given that LK 5...
 8.8.6.49: Use the diagram of ~WXYZ to find the indicated length. (p. 515) V 4...
 8.8.2.49: Decide if the side lengths form a triangle. If so, would the triang...
 8.8.4.50: COORDINATE GEOMETRY Use the given vertices to graph ~JKLM. Classify...
 8.8.6.50: Use the diagram of ~WXYZ to find the indicated length. (p. 515) V 4...
 8.8.2.50: Decide if the side lengths form a triangle. If so, would the triang...
 8.8.4.51: COORDINATE GEOMETRY Use the given vertices to graph ~JKLM. Classify...
 8.8.2.51: Decide if the side lengths form a triangle. If so, would the triang...
 8.8.4.52: REASONING Are all rhombuses similar? Are all squares similar? Expla...
 8.8.2.52: Decide if the side lengths form a triangle. If so, would the triang...
 8.8.4.53: CHALLENGE Quadrilateral ABCD shown at the right is a rhombus. Given...
 8.8.2.53: Decide if the side lengths form a triangle. If so, would the triang...
 8.8.4.54: MULTISTEP PROBLEM In the window shown at the right, }BD > }DF > }B...
 8.8.2.54: Decide if the side lengths form a triangle. If so, would the triang...
 8.8.2.55: Find the value of x. Write your answer in simplest radical form. (p...
 8.8.4.55: PATIO You want to mark off a square region in your yard for a patio...
 8.8.2.56: Find the value of x. Write your answer in simplest radical form. (p...
 8.8.4.56: PROVING THEOREM 8.11 Use the plan for proof below to write a paragr...
 8.8.2.57: Find the value of x. Write your answer in simplest radical form. (p...
 8.8.4.57: PROVING COROLLARIES Write the corollary as a conditional statement ...
 8.8.4.58: PROVING COROLLARIES Write the corollary as a conditional statement ...
 8.8.4.59: PROVING COROLLARIES Write the corollary as a conditional statement ...
 8.8.4.60: PROVING THEOREM 8.12 In Exercises 60 and 61, prove both parts of Th...
 8.8.4.61: PROVING THEOREM 8.12 In Exercises 60 and 61, prove both parts of Th...
 8.8.4.62: EXTENDED RESPONSE In ABCD, }AB i }CD , and }DB bisects ADC. a. Show...
 8.8.4.63: PROVING THEOREM 8.13 Write a coordinate proof of the following stat...
 8.8.4.64: CHALLENGE Write a coordinate proof of part of Theorem 8.13. GIVEN c...
 8.8.4.65: In nJKL, KL 5 54.2 centimeters. Point M is the midpoint of }JK and ...
 8.8.4.66: Find the sine and cosine of the indicated angle. Write each answer ...
 8.8.4.67: Find the sine and cosine of the indicated angle. Write each answer ...
 8.8.4.68: Find the value of x. (p. 507) 288 10681278x
 8.8.4.69: Find the value of x. (p. 507) 1208 1638155811781088
 8.8.4.70: Find the value of x. (p. 507) 758628888
Solutions for Chapter 8: Find Angle Measures in Polygons
Full solutions for Geometry (Holt McDougal Larson Geometry)  1st Edition
ISBN: 9780618595402
Solutions for Chapter 8: Find Angle Measures in Polygons
Get Full SolutionsGeometry (Holt McDougal Larson Geometry) was written by and is associated to the ISBN: 9780618595402. This textbook survival guide was created for the textbook: Geometry (Holt McDougal Larson Geometry), edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Since 347 problems in chapter 8: Find Angle Measures in Polygons have been answered, more than 26700 students have viewed full stepbystep solutions from this chapter. Chapter 8: Find Angle Measures in Polygons includes 347 full stepbystep solutions.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

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.