ch 8 review Name: Class: Date:

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1 Name: Class: Date: ID: A ch 8 review 1. How many triangles are formed by drawing diagonals from one vertex in the figure? Find the sum of the measures of the angles in the figure. a. 5, 900 b. 5, 1080 c. 6, 900 d. 6, The sum of the measures of the interior angles of a convex quadrilateral is. a. 180 b. 270 c. 360 d The measure of each interior angle of a regular hexagon is. a. 30 b. 120 c. 15 d. 60 1

2 Name: ID: A 4. The measure of each exterior angle of a regular octagon is. a b c. 45 d. 135 Find the value of x. (The figure may not be drawn to scale.) 5. a. 74 b. 108 c. 49 d Find the measure of each exterior angle of a regular polygon with 16 sides. a b. 360 c d Find the measure of one of the exterior angles of a regular polygon with nine sides. a. 140 b. 40 c. 160 d. 20 2

3 Name: ID: A 8. Find the measure of the missing angle. 9. Find the value of x. 10. Find x and y. 11. Find the sum of the measures of the interior angles in the figure. 12. A regular pentagon has five congruent interior angles. What is the measure of each angle? 13. What is the measure of each interior angle in a regular octagon? 3

4 Name: ID: A 14. Find the number of sides of a convex polygon if the measures of its interior angles have a sum of Find the number of sides of a regular polygon with each interior angle equal to Find the measure of an interior angle and an exterior angle of a regular polygon with 20 sides. 17. What is the measure of each exterior angle in a regular pentagon? Open-ended: 18. Using the drawing and the triangle sum theorem, explain why the sum of the measures of the interior angles of a pentagon is 540. Find the measure of an interior angle and the measure of an exterior angle for the regular polygon gon gon Find each unknown angle measure Consider an octagonal stop sign. a. Find the sum of the interior angles of a stop sign. b. Find the measure of one of the interior angles of a stop sign. c. Find the measure of an exterior angle of a stop sign. 4

5 Name: ID: A Writing: 24. Explain how the formula for finding the sum of the interior angles of a polygon can be derived. Open-ended: 25. Write an indirect proof to show that the measure of each interior angle of a regular hexagon is not Write an indirect proof to show that the measure of each interior angle of a regular decagon is SHORT RESPONSE Write your answer on a separate piece of paper. Figure ABCDE below is a regular pentagon. What is the measure, in degrees, of AFE? Explain in words how you arrived at your answer. 28. For parallelogram PQLM below, if m PML = 83, then m PQL =. a. m PQM b. 83 c. 97 d. m QLM 5

6 Name: ID: A 29. Consecutive angles in a parallelogram are always. a. congruent angles b. complementary angles c. supplementary angles d. vertical angles 30. Choose the statement that is NOT ALWAYS true. For any parallelogram. a. the diagonals bisect each other b. opposite angles are congruent c. the diagonals are perpendicular d. opposite sides are congruent 31. Find the value of the variables in the parallelogram. a. x = 52, y = 10.5, z = 159 b. x = 21, y = 55, z = 104 c. x = 55, y = 21, z = 104 d. x = 10.5, y = 52, z = If ON =7x 5, LM =6x + 3, NM =x 4, and OL =2y + 5, find the values of x and y given that LMNO is a parallelogram. a. x = 1 2 ; y = 13 c. x = 8; y = b. x = 8; y = 2 d. x = 2; y = 2 6

7 Name: ID: A 33. Complete the statement for parallelogram ABCD. Then state a definition or theorem as the reason. AD 34. Find AM in the parallelogram if PN = 10 and MO = Refer to the figure below. Given: UVWX is a parallelogram, m WXV = 17, m WVX = 29, XW = 41, UX = 24, UY = 15 a. Find m WVU. b. Find WV. c. Find m XUV. d. Find UW. 7

8 Name: ID: A 36. Use the figure below. Given: FGHJ is a parallelogram, m JHG = 68, JH = 34, GH = 19 a. Find m FJH. b. Find JF. c. Find m GFJ. d. Find FG. True or False: 37. If a quadrilateral is a parallelogram, then consecutive angles are complementary. 38. If a quadrilateral is a parallelogram, then opposite angles are complementary. Use the diagram to find the given length. 39. AC 40. BD 8

9 Name: ID: A 41. Complete the steps of this proof. Given: parallelogram WXYZ Prove: XYZ ZWX Statements Reasons 1. parallelogram WXYZ 1.? 2. WZ XY; WX YZ 2.? 3. WZX YXZ; WXZ YZX 3.? 4. ZX ZX 4.? 5. XYZ ZWX 5.? 42. SHORT RESPONSE Write your answer on a separate piece of paper. ABCD is a parallelogram. Find the value of x and explain your reasoning. (The figure may not be drawn to scale.) 43. (2, 3) and (3, 1) are opposite vertices in a parallelogram. If (0, 0) is the third vertex, then the fourth vertex is. a. 1, 1 5 b. 2, 2 c. 1, 2 d. 5, 4 9

10 Name: ID: A 44. Given the following, determine whether quadrilateral XYZW must be a parallelogram. Justify your answer. XY WZ and XW YZ. 45. Given: ABF DEC and FB EC Prove: BCEF is a parallelogram. 46. Given: ABCDF is a parallelogram and FB EC Prove: BCEF is a parallelogram. 10

11 Name: ID: A 47. Given: VU ST and SV TU Prove: VX = XT 48. Given: VU ST and VU ST Prove: VX = XT 49. Given: SV TU and SV TU Prove: VX = XT 11

12 Name: ID: A 50. Draw a figure in the coordinate plane and write a two-column coordinate proof. Given: Quadrilateral ABCD with A( 5, 0), B(4, 3), C(8, 1), D( 1, 2) Prove: ABCD is a parallelogram. 51. Use the distance formula to determine whether ABCD below is a parallelogram. 52. Use the Distance Formula to determine whether ABCD below is a parallelogram. 12

13 Name: ID: A 53. Given: ST UV and TU SV Prove: VX = XT Open-ended: 54. Find a fourth point, D, so that a parallelogram is formed using the vertices A 0, 4, B 5, 3, C 4, 3, and D in any order. Plot your point and draw the parallelogram in the coordinate plane. 55. SHORT RESPONSE Write your answer on a separate piece of paper. Is quadrilateral ABCD a parallelogram? Explain your answer briefly. (The figure may not be drawn to scale.) 13

14 Name: ID: A 56. Which statement is true? a. All quadrilaterals are squares. b. All rectangles are squares. c. All parallelograms are quadrilaterals. d. All quadrilaterals are parallelograms. 57. Choose the statement that is NOT ALWAYS true. For a rhombus. a. each diagonal bisects a pair of opposite angles b. all four sides are congruent c. the diagonals are congruent d. the diagonals are perpendicular 58. The diagonals of a parallelogram always. a. are congruent b. are parallel c. bisect each other d. are perpendicular 59. Which statement is NOT always true of a rhombus? a. The diagonals are perpendicular to each other. b. The diagonals bisect each other. c. Each diagonal is longer than at least one side. d. The sum of the diagonals is less than the perimeter. 60. Draw a Venn diagram showing the relationship between squares, rectangles, rhombuses, parallelograms, and quadrilaterals. 61. Consider the statement, "If a parallelogram is a square, then it is a rhombus." a. Decide whether it is true or false. b. Write the converse. c. Decide whether the converse is true or false. 62. If the diagonals of a parallelogram are perpendicular, then the parallelogram is also what type of figure? 63. If the diagonals of a parallelogram are equal in length, then the parallelogram is also what type of figure? 64. True or false: A rectangle is a parallelogram. 65. True or false: A quadrilateral has three diagonals. 66. True or false: A rhombus is a regular polygon. 67. True or false: A quadrilateral is a polygon with four angles. 68. True or false: A square is a rectangle. 69. True or false: In quadrilateral ABCD, AB and CD are adjacent sides. 14

15 Name: ID: A 70. True or false: Opposite angles in a parallelogram are supplementary. 71. True or false: Opposite sides of a parallelogram are congruent. 72. True or false: A rectangle is an equiangular quadrilateral. 73. True or false: The sum of the measures of the angles of a quadrilateral is 180. Open-ended: Give the possible coordinates of the vertices of the quadrilateral so that the diagonals lie on the x- and y-axes. 74. a rhombus with its horizontal diagonal longer than its vertical diagonal 75. a square with diagonals more than 10 units long 76. a rhombus with its horizontal diagonal shorter than its vertical diagonal 77. a square with diagonals more than 8 units long True or False: 78. All squares are quadrilaterals. 79. If a quadrilateral is a parallelogram, then it is a kite. 80. Quadrilateral DEFG is a rhombus. What is the value of x? You can use the following fact to help you: If two sides of a triangle are congruent, then the angles opposite them are congruent. (The figure may not be drawn to scale.) 81. Determine if the statement is a valid definition. If it is not, state a counterexample. A square is a figure with four right angles and four congruent sides. Decide if the argument is valid or invalid. Explain your reasoning. 82. If a figure is a rhombus, then it is a parallelogram. A square is a rhombus. Therefore, a square is a parallelogram. 15

16 Name: ID: A 83. Performance Task: Does showing that all four pairs of corresponding sides are congruent prove that two quadrilaterals are congruent? Explain why or why not. If not, what additional information would you need to show in order to prove the two quadrilaterals congruent? 84. EXTENDED RESPONSE Write your answer on a separate piece of paper. The coordinates of the vertices of a quadrilateral are A 8, 3, B 6, 3, C 3, 2, and D 5, 4. Part A How long is each side of the quadrilateral? Show your work. Part B What are the slopes of each side of the quadrilateral? Show your work. Part C What type of quadrilateral is it? Explain your reasoning. 85. Given: ABCD is a rhombus. Prove: ACB CAD 86. Writing: Explain the difference between a rhombus and a rectangle. 87. Is the biconditional "A quadrilateral is a square if and only if it is a rectangle" True or False? Explain your reasoning. 88. a. Is the statement "If a quadrilateral is a square, then it is a rectangle" True or False? b. State the converse, inverse, and contrapositive of the statement in part (a). Which, if any, of these is a true statement? 89. a. Is the statement "If a quadrilateral is a rectangle, then it is a parallelogram" True or False? b. Write the inverse of the statement in part (a) and tell if it is True or False. 90. a. Is the statement "If a quadrilateral is a square, then it is a rhombus" True or False? b. Write the contrapositive of the statement in part (a) and tell if it is True or False. 16

17 Name: ID: A Decide if the argument is valid or invalid. If the argument is valid, tell which rule of logic is used. If the argument is invalid, tell why. 91. If a quadrilateral is a rectangle, then it is a parallelogram. Quadrilateral ABCD is a parallelogram. Therefore, quadrilateral ABCD is a rectangle. Performance Task: 92. Graph the line y = 2x 3. Find the equations of three other lines that when graphed with y = 2x 3 enclose a rectangle on the coordinate plane. 93. Isosceles trapezoid JKLM has legs JK and LM, and base KL. If JK =8x 9, KL =7x + 10, and LM =10x + 2, find the value of x. a. 1 c. 19 b Choose the statement that is NOT always true. For an isosceles trapezoid. a. the diagonals are congruent b. the base angles are congruent c. the diagonals are perpendicular d. the legs are congruent d

18 Name: ID: A 95. For the trapezoid shown below, the measure of the midsegment is. a. 29 b. 58 c. 25 d Choose the figure below which satisfies the definition of a kite. a. c. b. d. 97. Which type of quadrilateral has no parallel sides? a. rectangle b. trapezoid c. rhombus d. kite 18

19 Name: ID: A 98. Three vertices of an isosceles trapezoid are shown in the figure below. What are the coordinates of the missing vertex that make the bases parallel to the x-axis? a. 2, 1 c. 2, 0 b. 3, 0 d. 3, In what type of trapezoid are the base angles congruent? 100. Given: Trapezoid ABCD with midsegment EF. If EF = 23 and DC = 26, find the length of AB One side of a kite is 5 cm less than 2 times the length of another. If the perimeter is 8 cm, find the length of each side of the kite. 19

20 Name: ID: A 102. Find m T in the diagram, if m R = 130 and m S = Writing: Write a paragraph proof. Given: kite EFGH Prove: F H 104. Writing: Write a paragraph proof. Given: kite EFGH Prove: FEG HEG Open-ended: Give the possible coordinates of the vertices of the quadrilateral so that the diagonals lie on the x- and y-axes a trapezoid 20

21 Name: ID: A Open-ended: 106. Use the Venn diagram below to compare and contrast the properties of a parallelogram and the properties of a kite. The intersection represents the properties that they have in common. Performance Task: 107. If an equilateral triangle with a side length of 1 unit is folded so that the vertex of the triangle touches the midpoint of the base, find the perimeter of the trapezoid formed. Open-ended: 108. Draw a kite in the coordinate plane. Show that your quadrilateral is a kite Show that quadrilateral ABCD with vertices A(0, 0), B(6, 0), C(5, 2), and D(1, 2) is an isosceles trapezoid Show that quadrilateral JKLM with vertices J 0, 0, K 3, 0, L 6, 2, and M 3, 2 is an isosceles trapezoid. 21

22 Name: ID: A 111. SHORT RESPONSE Write your answer on a separate piece of paper. Figure ABCD below is a trapezoid. Find the value of a, and then describe two ways to find the value of c and give its value The coordinates of quadrilateral PQRS are P( 3, 0), Q(0, 4), R(4, 1), and S(1, 3). What best describes the quadrilateral? a. a rectangle b. a square c. a rhombus d. a parallelogram 113. Use slope or the Distance Formula to determine the most precise name for the figure: A( 1, 4), B(1, 1), C(4, 1), D(2, 2). a. kite b. trapezoid c. rhombus d. square 114. If all four sides of a quadrilateral are congruent, the quadrilateral is. a. a kite b. a nonsquare rectangle c. a rhombus d. a trapezoid 115. What name best describes the quadrilateral? a. parallelogram b. rhombus c. kite d. rectangle 22

23 Name: ID: A 116. a. kite b. rectangle c. parallelogram d. triangle 117. Which statement is false? a. All rhombuses are kites. b. All squares are rhombuses. c. Every kite is a rectangle. d. All squares are quadrilaterals Which statement is false? a. Every square is a parallelogram. b. Some rhombuses are rectangles. c. Every rhombus is a quadrilateral. d. Every parallelogram is a rhombus Which statement is false? a. If a quadrilateral is a square, then it is not a kite. b. Some parallelograms are rhombuses. c. All parallelograms are quadrilaterals. d. If a quadrilateral is a rectangle, then it is a kite Describe the figure using as many of these words as possible: rectangle, trapezoid, square, quadrilateral, parallelogram, rhombus Identify the quadrilateral which has all sides and angles congruent. 23

24 Name: ID: A 122. Open-ended Problem: List all of the important characteristics of each quadrilateral. a. square b. rectangle c. parallelogram d. rhombus e. trapezoid f. kite 123. Quadrilateral ABCD has vertices A 2, 2, B 3, 2, C 6, 2, and D 1, 2. What type of quadrilateral is ABCD? 124. Quadrilateral ABCD has vertices A 2, 5, B 8, 5, C 6, 1, and D 0, 1. What type of quadrilateral is ABCD? Explain your reasoning Quadrilateral ABCD has vertices A 6, 2, B 0, 2, C 4, 2, and D 2, 6. What type of quadrilateral is ABCD? Explain your reasoning. Performance Task: 126. Draw a Venn diagram showing the relationships among the various types of quadrilaterals Theorem 8.18 says that if a quadrilateral is a kite, then its diagonals are perpendicular. Is the converse true? Justify your reasoning Prove that quadrilateral PQRS is a rhombus by showing that it is a parallelogram with perpendicular diagonals. 24

25 Name: ID: A 129. Prove quadrilateral HIJK is an isosceles trapezoid Prove quadrilateral HIJK is an isosceles trapezoid by showing it is a trapezoid with congruent diagonals Prove quadrilateral CDEF is a non-isosceles trapezoid. 25

26 Name: ID: A 132. Prove quadrilateral BCDE is an isosceles trapezoid In the diagram, m BAC = 30, m DCA = 110, BCA DAC, and AC BD. Is enough information given to show that quadrilateral ABCD is an isosceles trapezoid? Explain ABC CDA. What special type of quadrilateral is ABCD? Write a paragraph proof to support your conclusion. 26

27 ch 8 review Answer Section 1. ANS: A PTS: 1 DIF: Level B REF: MOT70179 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: diagonals sum interior angle measures of polygons BLM: Application 2. ANS: C PTS: 1 DIF: Level B REF: HLGM0440 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: sum quadrilateral interior angle measures of polygons BLM: Application 3. ANS: B PTS: 1 DIF: Level B REF: HLGM0441 STA: MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular polygon hexagon interior angle measures of polygons BLM: Application 4. ANS: C PTS: 1 DIF: Level B REF: HLGM0451 STA: MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: octagon regular polygon exterior angle measures of polygons BLM: Application 5. ANS: D PTS: 1 DIF: Level B REF: MLPA0713 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: exterior angle measures of polygons BLM: Application 6. ANS: C PTS: 1 DIF: Level B REF: GMPA0651 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular polygon exterior angle measures of polygons BLM: Application 7. ANS: B PTS: 1 DIF: Level B REF: AXGM0234 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular polygon interior angle measures of polygons BLM: Application 8. ANS: 114 PTS: 1 DIF: Level B REF: ACG60049 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: quadrilateral interior angle measures of polygons 9. ANS: 128 BLM: Application PTS: 1 DIF: Level B REF: MPPA1214 STA: MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: quadrilateral exterior angle measures of polygons BLM: Application 1

28 10. ANS: x = 103, y = 66 PTS: 1 DIF: Level B REF: PHGM0246 STA: MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: quadrilateral supplementary angles interior angle measures of polygons BLM: Application 11. ANS: 540 PTS: 1 DIF: Level B REF: PHGM0214 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: polygon sum interior angle measures of polygons 12. ANS: 108 BLM: Application PTS: 1 DIF: Level B REF: HLGM0437 STA: MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular polygon pentagon interior angle measures of polygons BLM: Application 13. ANS: 135 PTS: 1 DIF: Level B REF: HLGM0442 STA: MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular polygon octagon interior angle measures of polygons BLM: Application 14. ANS: 18 PTS: 1 DIF: Level B REF: AGEO0311 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: polygon sum interior angle measures of polygons 15. ANS: 40 PTS: 1 DIF: Level B REF: XEGS0702 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular polygon interior angle measures of polygons BLM: Application BLM: Application 2

29 16. ANS: interior angle: 162 degrees; exterior angle: 18 degrees PTS: 1 DIF: Level B REF: GGEO1003 STA: MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular polygon interior angle measures of polygons exterior angle measures of polygons BLM: Application 17. ANS: 72 PTS: 1 DIF: Level B REF: HLGM0444 STA: MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular pentagon exterior angle measures of polygons BLM: Application 18. ANS: Sample answer: By drawing all the diagonals possible from one vertex, the pentagon is divided into 3 triangles. Since the sum of the angles of each triangle is 180, the sum of the angles of the pentagon is 3 180, or 540. PTS: 1 DIF: Level B REF: MIM20457 STA: MI.MIGLC.MTH G1.4.4 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: sum interior angle measures of polygons pentagon BLM: Comprehension 19. ANS: 157.5, 22.5 PTS: 1 DIF: Level B REF: MLPA0709 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular polygon interior angle measures of polygons 20. ANS: about 168.8, about 11.2 PTS: 1 DIF: Level B REF: MLPA0710 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular polygon interior angle measures of polygons BLM: Application BLM: Application 3

30 21. ANS: 55, 60, 75, 80 PTS: 1 DIF: Level B REF: BS TOP: Lesson 8.1 Find Angle Measures in Polygons BLM: Application 22. ANS: 56, 84, 92, 128 PTS: 1 DIF: Level B REF: BS TOP: Lesson 8.1 Find Angle Measures in Polygons BLM: Application 23. ANS: a b. 135 c. 45 KEY: exterior angle measures of polygons KEY: exterior angle measures of polygons PTS: 1 DIF: Level A REF: PA SR.05 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: exterior angle measures of polygons interior angle measures of polygons sum regular polygon BLM: Application 24. ANS: Sample answer: By drawing all the diagonals from one vertex of a polygon, the polygon is divided into two fewer triangles than there are sides of the polygon (that is, n 2 triangles if n = the number of sides.) Since the sum of the measures of the angles of a triangle is 180, and since the angles of the polygon are formed by combinations of the angles of these triangles, the formula is S = (n 2)180. PTS: 1 DIF: Level B REF: MIM30157 STA: MI.MIGLC.MTH G1.4.4 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: polygon sum interior angle measures of polygons BLM: Comprehension 25. ANS: Sample answer: Assume that the measure of each interior angle of a regular hexagon is 150. Then the sum of the measures is 6(150 ) = 900. So, (n 2)180 = 900 and thus n 2 = 5, or n = 7. But this contradicts the fact that a hexagon has 6 sides. Therefore, the assumption is false and it must be true that the measure of each interior angle of a regular hexagon is not 150. PTS: 1 DIF: Level B REF: MIM30184 NAT: NCTM 9-12.REA.3 NCTM 9-12.REA.4 STA: MI.MIGLC.MTH L3.3.2 MI.MIGLC.MTH G1.4.4 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: interior angle measures of polygons hexagon proof indirect BLM: Analysis 4

31 26. ANS: Sample answer: Assume that the measure of each interior angle of a regular decagon is not 144. Then, since a decagon has 10 sides, the sum of the measures of the interior angles is not 10(144 ) or So (n 2) and thus n 2 8, and n 10. But this contradicts the fact that a decagon does have 10 sides. Therefore, the assumption is false and it is true that the measure of each interior angle of a regular decagon is 144. PTS: 1 DIF: Level B REF: MIM30185 NAT: NCTM 9-12.REA.3 NCTM 9-12.REA.4 STA: MI.MIGLC.MTH L3.3.2 MI.MIGLC.MTH G1.4.4 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: proof indirect interior angle measures of polygons BLM: Analysis 27. ANS: The measure of AFE is 108. Pentagon sides AE and AB are congruent because ABCDE is a regular pentagon. Thus, EAB is isosceles. The measure of EAB is 108, because each interior angle of a regular pentagon has a measure of 540 5, or 108. That leaves 72 for the sum of the measures of the two congruent base angles AEF and ABF, so the measure of AEF is half of 72, or 36. Triangle EDA is congruent to triangle EAB, because two sides and the included angle in EDA are congruent to two sides and the included angle in EAB. That means that the measure of EAF is 36, because EAF AEF. In EAF, m AFE = 180 m EAF m AEF, so the measure of AFE is 108 : = 108. PTS: 1 DIF: Level C REF: MC NAT: NCTM 9-12.GEO.1.c NCTM 9-12.REA.4 NCTM 9-12.REA.3 STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G1.5.2 MI.MIGLC.MTH G2.3.1 MI.MIGLC.MTH G2.3.2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: pentagon regular polygon explain BLM: Analysis 28. ANS: B PTS: 1 DIF: Level B REF: HLGM0457 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: angle measure parallelogram BLM: Comprehension 29. ANS: C PTS: 1 DIF: Level A REF: MLGE0285 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: parallelogram consecutive interior angles property BLM: Comprehension 30. ANS: C PTS: 1 DIF: Level B REF: MHST0010 MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: property parallelogram BLM: Comprehension 5

32 31. ANS: B PTS: 1 DIF: Level B REF: MHN90085 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH G1.1.2 MI.MIGLC.MTH G1.2.1 MI.MIGLC.MTH G1.2.2 MI.MIGLC.MTH G1.4.1 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: angle measure parallelogram diagonals BLM: Application 32. ANS: C PTS: 1 DIF: Level B REF: MLGE0400 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: side lengths parallelogram BLM: Application 33. ANS: BC, the opposite sides of a parallelogram are congruent PTS: 1 DIF: Level B REF: GGEO0601 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: property parallelogram BLM: Comprehension 34. ANS: 9.5 PTS: 1 DIF: Level B REF: PHGM0902 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: parallelogram diagonal BLM: Application 35. ANS: a. 46 b. 24 c. 134 d. 30 PTS: 1 DIF: Level B REF: MLGE0132 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 MI.MIGLC.MTH G1.4.4 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: angle measure parallelogram diagonals side lengths BLM: Application 6

33 36. ANS: a. 112 b. 19 c. 68 d. 34 PTS: 1 DIF: Level B REF: MLGE0133 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 MI.MIGLC.MTH G1.4.4 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: angle measure parallelogram diagonals side lengths BLM: Application 37. ANS: False PTS: 1 DIF: Level A REF: MIM20428 MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: parallelogram property BLM: Comprehension 38. ANS: False PTS: 1 DIF: Level A REF: MIM20430 MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: parallelogram property BLM: Comprehension 39. ANS: 10 PTS: 1 DIF: Level B REF: 7f5cc4e2-cdbb-11db-b f7 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: Parallelogram bisect diagonal BLM: Knowledge 40. ANS: 8 PTS: 1 DIF: Level B REF: 7f5dd6e7-cdbb-11db-b f7 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: Parallelogram bisect diagonal BLM: Knowledge 7

34 41. ANS: Statements Reasons 1. parallelogram WXYZ 1. Given 2. WZ XY; WX YZ 2. Definition of parallelogram 3. WZX YXZ; WXZ YZX 3. If 2 parallellines are intersected by a transversal, then alternate interior angles are congruent. 4. ZX ZX 4. Reflexive Property 5. XYZ ZWX 5. ASA Postulate PTS: 1 DIF: Level B REF: BS NAT: NCTM 9-12.REA.4 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: triangle parallelogram proof BLM: Analysis 42. ANS: The fact that ABCD is a parallelogram means that AB and CD are parallel. That leads to m DCB = m EBC = 132, because m DCB and m EBC are congruent alternate interior angles formed by a transversal through parallel lines. Because of angle addition, m DCB = 51 + x. Using substitution, 51 + x = 132, so x = = 81. PTS: 1 DIF: Level B REF: MCT90009 NAT: NCTM 9-12.ALG.2.b NCTM 9-12.GEO.1.c NCTM 9-12.GEO.1.a NCTM 9-12.REA.4 NCTM 9-12.REA.3 STA: MI.MIGLC.MTH G1.1.2 MI.MIGLC.MTH G1.4.1 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: angle measure parallelogram interior exterior BLM: Analysis 43. ANS: D PTS: 1 DIF: Level B REF: MLGE0286 STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: vertices coordinates parallelogram BLM: Application 44. ANS: Yes. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. PTS: 1 DIF: Level B REF: AD MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: parallelogram quadrilateral justify diagonals BLM: Application 8

35 45. ANS: 1. ABF DEC 1. Given 2. BF EC 2. Corresponding Parts of are. 3. FB EC 3. Given 4. BCEF is a parallelogram. 4. If 1 pair of opposite sides are and, then the quadrilateral is a parallelogram. PTS: 1 DIF: Level B REF: MLGE0301A NAT: NCTM 9-12.REA.4 NCTM 9-12.GEO.1.c NCTM 9-12.REA.3 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: triangle parallelogram parallel lines congruence proof CPCTC BLM: Analysis 46. ANS: 1. ACDF is a parallelogram 1. Given 2. FE CB 2. Definition of a parallelogram 3. FB EC 3. Given 4. BCEF is a parallelogram. 4. Definition of a parallelogram PTS: 1 DIF: Level B REF: MLGE0301B NAT: NCTM 9-12.REA.4 NCTM 9-12.GEO.1.c NCTM 9-12.REA.3 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: triangle parallelogram parallel lines congruence proof CPCTC BLM: Analysis 47. ANS: 1. VU ST and SV TU 1. Given 2. STUV is a parallelogram. 2. If both pairs of opp. sides of a quad. are, then the quad. is a parallelogram. 3. VX = XT 3. The diagonals of a parallelogram bisect each other. PTS: 1 DIF: Level C REF: XEGS0704A NAT: NCTM 9-12.REA.3 NCTM 9-12.REA.4 NCTM 9-12.GEO.1.c TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: parallelogram congruent proof diagonals BLM: Analysis 9

36 48. ANS: 1. VU ST and VU ST 1. Given 2. STUV is a parallelogram. 2. If one pair of opp. sides of a quad. are both and, then the quad. is a parallelogram. 3. VX = XT 3. The diagonals of a parallelogram bisect each other. PTS: 1 DIF: Level C REF: XEGS0704B NAT: NCTM 9-12.REA.3 NCTM 9-12.REA.4 NCTM 9-12.GEO.1.c TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: parallelogram congruent proof diagonals BLM: Analysis 49. ANS: 1. SV TU and SV TU 1. Given 2. STUV is a parallelogram. 2. If one pair of opp. sides of a quad. are both and, then the quad. is a parallelogram. 3. VX = XT 3. The diagonals of a parallelogram bisect each other. PTS: 1 DIF: Level C REF: XEGS0704C NAT: NCTM 9-12.REA.3 NCTM 9-12.REA.4 NCTM 9-12.GEO.1.c TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: parallelogram congruent proof diagonals BLM: Analysis 10

37 50. ANS: 1. Quadrilateral ABCD with A 5, 0, B 4, 3, C 8, 1, D 1, 2 2. slope of AB = = 3 9 slope of BC = 1 ( 3) 8 4 = 2 4 slope of CD = 2 ( 1) 1 8 = 3 9 slope of AD = ( 1) = 2 4 = Given 2. Definition of slope 3. AB DC, AD BC 3. Lines with = slopes are. 4. ABCD is a parallelogram. 4. Definition of a parallelogram PTS: 1 DIF: Level B REF: MLGE0302 NAT: NCTM 9-12.GEO.1.c NCTM 9-12.GEO.4.a NCTM 9-12.REA.3 NCTM 9-12.GEO.2.a NCTM 9-12.REA.4 STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.2 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: slope coordinate proof two-column coordinate geometry BLM: Analysis 11

38 51. ANS: Since AB = CD =3 10 and BC = AD = 8, ABCD is a parallelogram. PTS: 1 DIF: Level B REF: MLGE0287 NAT: NCTM 9-12.GEO.2.a STA: MI.MIGLC.MTH A1.2.9 MI.MIGLC.MTH G1.1.5 MI.MIGLC.MTH G1.4.1 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G1.4.3 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: parallelogram distance formula coordinate geometry BLM: Evaluation 52. ANS: If ABCD is a parallelogram, then AB = DC. Since AB = 37 and DC = 40, ABCD is not a parallelogram. PTS: 1 DIF: Level B REF: MLGE0288 NAT: NCTM 9-12.GEO.2.a STA: MI.MIGLC.MTH A1.2.9 MI.MIGLC.MTH G1.1.5 MI.MIGLC.MTH G1.4.1 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G1.4.3 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: parallelogram distance formula coordinate geometry BLM: Evaluation 53. ANS: 1. ST UV and TU SV 1. Given 2. STUV is a parallelogram. 2. Def. of a parallelogram 3. VX = XT 3. The diagonals of a parallelogram bisect each other. PTS: 1 DIF: Level B REF: MLGM0038 NAT: NCTM 9-12.REA.4 NCTM 9-12.REA.3 NCTM 9-12.GEO.1.c STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.2 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: parallelogram parallel lines proof BLM: Analysis 54. ANS: Three answers are possible: D 1 1, 2, D 9, 4 2, or D 9, 4 3. Check students' graphs. PTS: 1 DIF: Level B REF: MGEO0039 NAT: NCTM 9-12.GEO.4.a NCTM 9-12.GEO.2.a STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: parallelogram plot vertices coordinates BLM: Synthesis 12

39 55. ANS: Quadrilateral ABCD is not a parallelogram: The angles in any quadrilateral must have a sum of 360. The angles indicated have a sum of , which is 322. That means that m ABC = , so m ABC = 38. The measures of the opposite angles of a parallelogram must be equal, but m ABC m ADC. The quadrilateral is not a parallelogram. PTS: 1 DIF: Level B REF: MCT90280 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 MI.MIGLC.MTH G1.4.4 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: parallelogram property angle measures in polygons BLM: Evaluation 56. ANS: C PTS: 1 DIF: Level A REF: TASH0019 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH G1.4.3 KEY: property quadrilateral geometric figure BLM: Knowledge 57. ANS: C PTS: 1 DIF: Level B REF: HLGM0475 MI.MIGLC.MTH G1.4.3 KEY: property rhombus BLM: Comprehension 58. ANS: C PTS: 1 DIF: Level A REF: MLGE0291 MI.MIGLC.MTH G1.4.3 KEY: parallelogram bisect diagonal BLM: Knowledge 59. ANS: C PTS: 1 DIF: Level B REF: MC MI.MIGLC.MTH G1.4.3 KEY: property rhombus BLM: Comprehension 60. ANS: Diagrams vary. PTS: 1 DIF: Level B REF: HLGM0470 KEY: square rectangle parallelogram rhombus quadrilateral Venn diagram BLM: Comprehension 13

40 61. ANS: a. True. b. If a parallelogram is a rhombus, then it is a square. c. False. PTS: 1 DIF: Level B REF: MLGE0134 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH L3.2.1 MI.MIGLC.MTH L3.2.4 MI.MIGLC.MTH G1.4.3 KEY: property parallelogram rhombus converse BLM: Application 62. ANS: A rhombus PTS: 1 DIF: Level A REF: HLGM0471 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 KEY: perpendicular parallelogram rhombus diagonal BLM: Knowledge 63. ANS: A rectangle PTS: 1 DIF: Level A REF: MLGE0290 MI.MIGLC.MTH G1.4.3 KEY: rectangle parallelogram diagonal BLM: Knowledge 64. ANS: True PTS: 1 DIF: Level A REF: DJAF1009A NAT: NCTM 9-12.GEO.1.a KEY: polygon triangle quadrilateral true false BLM: Knowledge 65. ANS: False PTS: 1 DIF: Level A REF: DJAF1009B NAT: NCTM 9-12.GEO.1.a KEY: polygon triangle quadrilateral true false BLM: Knowledge 66. ANS: False PTS: 1 DIF: Level A REF: DJAF1009C NAT: NCTM 9-12.GEO.1.a KEY: polygon triangle quadrilateral true false BLM: Knowledge 14

41 67. ANS: True PTS: 1 DIF: Level A REF: DJAF1009D NAT: NCTM 9-12.GEO.1.a KEY: polygon triangle quadrilateral true false BLM: Knowledge 68. ANS: True PTS: 1 DIF: Level A REF: DJAF1009F NAT: NCTM 9-12.GEO.1.a KEY: polygon triangle quadrilateral true false BLM: Knowledge 69. ANS: False PTS: 1 DIF: Level A REF: DJAF1009H NAT: NCTM 9-12.GEO.1.a KEY: polygon triangle quadrilateral true false BLM: Knowledge 70. ANS: False PTS: 1 DIF: Level A REF: DJAF1009I NAT: NCTM 9-12.GEO.1.a KEY: polygon triangle quadrilateral true false BLM: Knowledge 71. ANS: True PTS: 1 DIF: Level A REF: DJAF1009J NAT: NCTM 9-12.GEO.1.a KEY: polygon triangle quadrilateral true false BLM: Knowledge 72. ANS: True PTS: 1 DIF: Level A REF: DJAF1009K NAT: NCTM 9-12.GEO.1.a KEY: polygon triangle quadrilateral true false BLM: Knowledge 73. ANS: False PTS: 1 DIF: Level A REF: DJAF1009L NAT: NCTM 9-12.GEO.1.a KEY: polygon triangle quadrilateral true false BLM: Knowledge 15

42 74. ANS: Sample answer: ( 5, 0), (0, 3), (5, 0), (0, 3) PTS: 1 DIF: Level B REF: BS NAT: NCTM 9-12.GEO.2.a NCTM 9-12.GEO.4.a STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 KEY: vertices coordinate rhombus quadrilateral diagonal TEKSd2A BLM: Application 75. ANS: Sample answer: ( 6, 0), (0, 6), (6, 0), (0, 6) PTS: 1 DIF: Level B REF: BS NAT: NCTM 9-12.GEO.2.a NCTM 9-12.GEO.4.a STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 KEY: TEKSd2A BLM: Application 76. ANS: Sample answer: ( 3, 0), (0, 5), (3, 0), (0, 5) PTS: 1 DIF: Level B REF: BS NAT: NCTM 9-12.GEO.2.a NCTM 9-12.GEO.4.a STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 KEY: vertices coordinate rhombus quadrilateral TEKSd2A BLM: Application 77. ANS: Sample answer: ( 6, 0), (0, 6), (6, 0), (0, 6) PTS: 1 DIF: Level B REF: BS NAT: NCTM 9-12.GEO.2.a NCTM 9-12.GEO.4.a STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 KEY: square coordinate quadrilateral diagonal TEKSd2A BLM: Application 78. ANS: True PTS: 1 DIF: Level B REF: MIM20276 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH G1.4.3 KEY: square rectangle classify quadrilateral kite BLM: Application 16

43 79. ANS: False PTS: 1 DIF: Level A REF: MIM20278 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: classify conditional quadrilateral logic BLM: Comprehension 80. ANS: 57 PTS: 1 DIF: Level B REF: MCT90011 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH G1.2.1 MI.MIGLC.MTH G1.2.2 MI.MIGLC.MTH G1.4.1 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G1.4.3 KEY: solve angle rhombus BLM: Application 81. ANS: a valid definition PTS: 1 DIF: Level B REF: MGEO0004 NAT: NCTM 9-12.GEO.1.c NCTM 9-12.GEO.1.a NCTM 9-12.REA.2 STA: MI.MIGLC.MTH L3.1.3 MI.MIGLC.MTH L3.3.2 MI.MIGLC.MTH L3.3.3 KEY: counterexample definition BLM: Comprehension 82. ANS: valid; Law of Syllogism PTS: 1 DIF: Level C REF: MIM20402 NAT: NCTM 9-12.GEO.1.c NCTM 9-12.COM.3 NCTM 9-12.REA.3 STA: MI.MIGLC.MTH L3.1.2 MI.MIGLC.MTH L3.2.3 MI.MIGLC.MTH L3.3.1 MI.MIGLC.MTH L3.3.3 KEY: conditional logic BLM: Evaluation 83. ANS: No; for example, a rhombus with sides of length 6 cm and angles measuring 30, 150, 30, and 150 is not congruent to a square with sides of length 6 cm, even though all four pairs of corresponding sides are congruent. The necessary additional information needed to prove congruence would be either three pairs of corresponding angles congruent or two pairs of adjacent corresponding angles congruent. PTS: 1 DIF: Level B REF: BS STA: MI.MIGLC.MTH G2.3.2 KEY: write quadrilateral congruent proof BLM: Evaluation 17

44 84. ANS: Part A AB = BC = CD = AD = = = = = 10 Part B slope of AB = = 3 slope of BC = 3 6 = 1 3 slope of CD = = slope of AD = 5 8 = 1 3 Part C The quadrilateral is a rectangle. Answers will vary. PTS: 1 DIF: Level B REF: MC NAT: NCTM 9-12.GEO.2.a NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH A1.2.9 MI.MIGLC.MTH G1.1.5 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 KEY: square slope identify distance coordinate parallelogram rhombus quadrilateral BLM: Application 85. ANS: 1. ABCD is a rhombus. 1. Given 2. ABCD is a parallelogram. 2. Definition of a rhombus 3. AB CD; BC AD 3. Opposite sides of a parallelogram are congruent. 4. AC AC 4. Reflexive Property 5. ACB CAD 5. SSS Congruence Postulate PTS: 1 DIF: Level B REF: MLGE0303 NAT: NCTM 9-12.GEO.1.c NCTM 9-12.REA.3 NCTM 9-12.REA.4 STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.2 KEY: rhombus diagonal proof BLM: Analysis 18

45 86. ANS: Sample answer: A rhombus is a quadrilateral with four congruent sides while a rectangle is a quadrilateral with four right angles. PTS: 1 DIF: Level B REF: BS MI.MIGLC.MTH G1.4.3 KEY: rectangle rhombus quadrilateral TEKSc1 BLM: Comprehension 87. ANS: False; the conditional "If a quadrilateral is a rectangle, then it is a square" is false. Not all rectangles are squares. PTS: 1 DIF: Level B REF: MIM20411 NAT: NCTM 9-12.REA.1 NCTM 9-12.COM.3 NCTM 9-12.PRS.4 STA: MI.MIGLC.MTH L1.1.3 MI.MIGLC.MTH L3.2.1 MI.MIGLC.MTH A1.2.4 MI.MIGLC.MTH A1.2.5 MI.MIGLC.MTH A1.2.6 MI.MIGLC.MTH A1.2.7 MI.MIGLC.MTH A1.2.8 KEY: conditional logic BLM: Comprehension 88. ANS: a. True b. Converse: If a quadrilateral is a rectangle, then it is a square. Inverse: If a quadrilateral is not a square, then it is not a rectangle. Contrapositive: If a quadrilateral is not a rectangle, then it is not a square. The contrapositive is true. PTS: 1 DIF: Level C REF: MGEO0049 KEY: inverse converse contrapositive BLM: Application 89. ANS: a. True b. If a quadrilateral is not a rectangle, then it is not a parallelogram. False PTS: 1 DIF: Level B REF: MGEO0050 KEY: inverse conditional BLM: Application 90. ANS: a. True b. If a quadrilateral is not a rhombus, then it is not a square. True PTS: 1 DIF: Level B REF: MGEO0051 KEY: conditional contrapositive BLM: Application 19

46 91. ANS: invalid; converse error (ABCD could be a rhombus.) PTS: 1 DIF: Level C REF: MIM20405 NAT: NCTM 9-12.COM.3 NCTM 9-12.GEO.1.c NCTM 9-12.REA.3 STA: MI.MIGLC.MTH L3.1.2 MI.MIGLC.MTH L3.2.1 MI.MIGLC.MTH L3.2.3 MI.MIGLC.MTH L3.2.4 MI.MIGLC.MTH L3.3.1 MI.MIGLC.MTH L3.3.3 KEY: logic BLM: Evaluation 92. ANS: Equations may vary. Sample equations are given; y = 1 2 x 3, y = 2x + 2, y = 1 2 x + 2. PTS: 1 DIF: Level B REF: MIM20647 NAT: NCTM 9-12.GEO.4.a NCTM 9-12.GEO.2.a STA: MI.MIGLC.MTH A3.1.2 MI.MIGLC.MTH A3.1.4 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 KEY: line graph slope parallel perpendicular BLM: Application 93. ANS: B PTS: 1 DIF: Level C REF: MLGE0294 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: isosceles trapezoid leg BLM: Application 94. ANS: C PTS: 1 DIF: Level B REF: MHST0015 STA: MI.MIGLC.MTH G1.4.1 MI.MIGLC.MTH G1.4.2 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: property isosceles trapezoid BLM: Comprehension 20

47 95. ANS: A PTS: 1 DIF: Level B REF: MHST0016 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: trapezoid midsegment BLM: Application 96. ANS: B PTS: 1 DIF: Level A REF: MLGE0045 MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: identify kite BLM: Knowledge 97. ANS: D PTS: 1 DIF: Level B REF: HLGM0492 MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: side parallel quadrilateral kite BLM: Comprehension 98. ANS: D PTS: 1 DIF: Level B REF: MC STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: vertex coordinate geometry isosceles trapezoid BLM: Application 99. ANS: an isosceles trapezoid PTS: 1 DIF: Level A REF: MHST0018 STA: MI.MIGLC.MTH G1.4.1 MI.MIGLC.MTH G1.4.2 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: property isosceles trapezoid BLM: Knowledge 100. ANS: 20 PTS: 1 DIF: Level B REF: MHGM0064 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: midsegment trapezoid BLM: Application 101. ANS: 3 cm, 1 cm PTS: 1 DIF: Level B REF: MLGE0328 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: perimeter side kite BLM: Application 21

48 102. ANS: 110 PTS: 1 DIF: Level B REF: MLGE0097 NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.3 MI.MIGLC.MTH G1.4.4 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: angle measure kite 103. ANS: Sample answer: Since it is given that EFGH is a kite, then EF EH and GF GH because a kite has two pairs of congruent adjacent sides. Also, EG EG by the Reflexive Property. So, by the SSS Postulate, EFG EHG. Therefore, by the definition of congruent triangles, F H. PTS: 1 DIF: Level B REF: BS NAT: NCTM 9-12.REA.4 NCTM 9-12.REA.3 NCTM 9-12.GEO.1.c STA: MI.MIGLC.MTH G1.4.2 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: kite proof congruent angles congruent triangles SSS BLM: Analysis 104. ANS: Sample answer: Since it is given that EFGH is a kite, then EF EH and GF GH because a kite has two pairs of congruent adjacent sides. Also, EG EG by the Reflexive Property. So, by the SSS Postulate, EFG EHG. Therefore, by the definition of congruent triangles, FEG HEG. PTS: 1 DIF: Level B REF: BS NAT: NCTM 9-12.GEO.1.c NCTM 9-12.REA.4 NCTM 9-12.REA.3 STA: MI.MIGLC.MTH G1.4.2 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: kite proof congruent angles SSS congruent triangles BLM: Analysis 105. ANS: Sample answer: ( 3, 0), (0, 3), (7, 0), (0, 7) PTS: 1 DIF: Level B REF: BS NAT: NCTM 9-12.GEO.4.a NCTM 9-12.GEO.2.a STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: vertices coordinate geometry trapezoid diagonal BLM: Application 106. ANS: Answers may vary. A sample answer is given. Contrasting properties: In a kite, there are two pairs of adjacent sides of equal length; in a parallelogram, there are two pairs of opposite sides of equal length. Matching properties: Kites and parallelograms are both quadrilaterals. PTS: 1 DIF: Level B REF: MIM10695 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: compare Venn diagram property BLM: Comprehension 22

49 107. ANS: Notice in the figure that the portion of the triangle folded down has sides of length 1. Therefore, the 2 perimeter of the trapezoid is = units. PTS: 1 DIF: Level C REF: MIM10696 STA: MI.MIGLC.MTH G1.4.1 MI.MIGLC.MTH G1.5.2 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: equilateral triangle perimeter trapezoid BLM: Synthesis 108. ANS: Figures may vary. Sample answer: For the figure shown, AB = AD = 5 and BC = CD = 13. Therefore, since two distinct pairs of consecutive sides are equal in measure, quadrilateral ABCD is a kite. PTS: 1 DIF: Level B REF: MGEO0038 NAT: NCTM 9-12.GEO.4.a NCTM 9-12.GEO.2.a STA: MI.MIGLC.MTH A1.2.9 MI.MIGLC.MTH G1.1.5 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: prove coordinate geometry kite BLM: Application 23

50 109. ANS: AB= (6 0) = 6; BC= (5 6) = 5; CD= (1 5) = 4; AD= (1 0) = 5; slope of AB: = 0; slope of CD: = 0; Since the slopes of AB and CD are equal, ABCD is a trapezoid. Since BC = AD, ABCD is an isosceles trapezoid. PTS: 1 DIF: Level B REF: MIM30148 NAT: NCTM 9-12.PRS.4 NCTM 9-12.GEO.2.a STA: MI.MIGLC.MTH L1.1.3 MI.MIGLC.MTH L1.1.4 MI.MIGLC.MTH L1.3.1 MI.MIGLC.MTH A1.2.4 MI.MIGLC.MTH A1.2.5 MI.MIGLC.MTH A1.2.6 MI.MIGLC.MTH A1.2.7 MI.MIGLC.MTH A1.2.8 MI.MIGLC.MTH A1.2.9 MI.MIGLC.MTH A3.1.4 MI.MIGLC.MTH G1.1.5 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: isosceles trapezoid coordinate geometry proof BLM: Analysis 110. ANS: JK= (3 0) = 3; KL= (6 3) = 13; LM= ( 3 6) = 9; JM = = 13; slope of JK: = 0; slope of LM: 2 2 = 0; Since the slopes of JK 3 6 and LM are equal, JKLM is a trapezoid. Since KL = JM, JKLM is an isosceles trapezoid. PTS: 1 DIF: Level B REF: MIM30149 NAT: NCTM 9-12.GEO.2.a NCTM 9-12.PRS.4 STA: MI.MIGLC.MTH L1.1.3 MI.MIGLC.MTH L1.1.4 MI.MIGLC.MTH L1.3.1 MI.MIGLC.MTH A1.2.4 MI.MIGLC.MTH A1.2.5 MI.MIGLC.MTH A1.2.6 MI.MIGLC.MTH A1.2.7 MI.MIGLC.MTH A1.2.8 MI.MIGLC.MTH A1.2.9 MI.MIGLC.MTH A3.1.4 MI.MIGLC.MTH G1.1.5 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: isosceles trapezoid coordinate geometry proof BLM: Analysis 111. ANS: The value of a is 119. The value of c can be found from the fact that sides AB and DC are parallel. That means that c = 180, so c = = 56. Another way to find the value of c is to use the fact that the vertex angles of the trapezoid must total 360 : c + 61 = 360, so c = = 56. PTS: 1 DIF: Level B REF: MC NAT: NCTM 9-12.GEO.1.a MI.MIGLC.MTH G1.4.4 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: angle measure trapezoid BLM: Analysis 24

51 112. ANS: B PTS: 1 DIF: Level B REF: HLGM0476 STA: MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: coordinate geometry quadrilateral BLM: Comprehension 113. ANS: C PTS: 1 DIF: Level B REF: MGEO0011 NAT: NCTM 9-12.GEO.2.a NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH A1.2.9 MI.MIGLC.MTH G1.1.5 MI.MIGLC.MTH G1.4.2 MI.MIGLC.MTH G2.3.4 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: slope identify distance formula quadrilateral BLM: Comprehension 114. ANS: C PTS: 1 DIF: Level A REF: MHST0017 MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: property quadrilateral BLM: Knowledge 115. ANS: A PTS: 1 DIF: Level A REF: MIM10065 NAT: NCTM 9-12.GEO.1.a TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: quadrilateral identify BLM: Knowledge 116. ANS: A PTS: 1 DIF: Level A REF: MIM10066 NAT: NCTM 9-12.GEO.1.a TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: quadrilateral identify BLM: Knowledge 117. ANS: C PTS: 1 DIF: Level B REF: MIM20279 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: classify quadrilateral BLM: Comprehension 118. ANS: D PTS: 1 DIF: Level B REF: MIM20280 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: classify quadrilateral BLM: Comprehension 119. ANS: D PTS: 1 DIF: Level B REF: MIM20281 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: classify quadrilateral BLM: Comprehension 120. ANS: trapezoid, quadrilateral PTS: 1 DIF: Level A REF: MLGE0401 NAT: NCTM 9-12.GEO.1.a TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: square rectangle parallelogram rhombus trapezoid quadrilateral BLM: Knowledge 121. ANS: square PTS: 1 DIF: Level A REF: MPMC0708 MI.MIGLC.MTH G1.4.3 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: identify quadrilateral BLM: Knowledge 25