Quadrilaterals Chapter Questions
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1 1. What is a polygon? Quadrilaterals Chapter Questions 2. What are the properties of a parallelogram? 3. What are the special parallelograms and their unique properties? 4. Describe the difference of a parallelogram and a trapezoid? 5. Can you explain why a rhombus is a kite? Geometry - Quadrilaterals ~1~ NJCTL.org
2 Quadrilaterals Chapter Problems Angles of Polygons Classwork 1. Describe the polygon By sides Identify as convex or concave Tell whether the polygon is equilateral, equiangular, or regular. a. b. c. d. 2. What is the sum of the measures of the interior angles of a 14-gon? 3. What is the sum of the measures of the interior angles of a 52-gon? 4. Find the measure of each angle of the polygon. 5. What is the measure of each interior angle of a regular 20-gon? 6. What is the measure of each interior angle of a regular 40-gon? 7. What is the measure of each exterior angle of a regular 30-gon? 8. The measure of each angle of a regular convex polygon is 168 o. Find the number of the sides of the polygon. Homework 9. Describe the polygon By sides Identify as convex or concave Tell whether the polygon is equilateral, equiangular, or regular. Geometry - Quadrilaterals ~2~ NJCTL.org
3 a. b. c. d. 10. What is the sum of the measures of the interior angles of an 18-gon? 11. What is the sum of the measures of the interior angles of a 44-gon? 12. Find the value of each angle of the polygon. 13. What is the measure of each interior angle of a regular 35-gon? 14. What is the measure of each interior angle of a regular 27-gon? 15. What is the measure of each exterior angle of a regular 24-gon? 16. The measure of each angle of a regular convex polygon is 171 o. Find the number of the sides of the polygon. Properties of Parallelograms Classwork Decide whether the figure is a parallelogram. If yes, explain why Geometry - Quadrilaterals ~3~ NJCTL.org
4 18. The figure is a parallelogram. Find w, x, y, and z. 19. PQRS is a parallelogram. Answer the questions below. 20. If PQ = 17, then SR =. 21. If m R = 73 o, then m Q = and the m P =. 22. If PT = 5, then TR = and PR =. 23. If QS = 19, then ST =. 24. If PS = 2x 2 5 and QR = 13, then x =. Homework Decide whether the figure is a parallelogram. If yes, explain why The figure is a parallelogram. Find w, x, y, and z. 27. Geometry - Quadrilaterals ~4~ NJCTL.org
5 PQRS is a parallelogram. Answer the questions below. 28. If m Q = 126 o, then m R = and the m P =. 29. If QR = 17, then SP =. 30. If SQ = 27, then ST = and TQ =. 31. If PT = 11, then PR =. 32. If SR = and PQ = 15, then x =. Proving Quadrilaterals are Parallelograms Classwork Decide whether the quadrilateral is a parallelogram. If yes, state the theorem Geometry - Quadrilaterals ~5~ NJCTL.org
6 38. Homework Geometry - Quadrilaterals ~6~ NJCTL.org
7 Constructing Parallelograms Classwork 45. Construct a parallelogram in the space below. Justify why your construction is a parallelogram. Homework 46. Construct a parallelogram in the plane below. Justify why your construction is a parallelogram. Rhombi, Rectangles, and Squares Classwork 47. DEFG is a rhombus. Find x. 48. DEFG is a square. Find x. Geometry - Quadrilaterals ~7~ NJCTL.org
8 49. DEFG is a square. Find x. 50. DEFG is a rectangle. Find the length of each side. 51. DEFG is a rhombus. Find x. 52. DEFG is a rectangle. Find DF. Geometry - Quadrilaterals ~8~ NJCTL.org
9 53. DEFG is a square. Find DG. Round to the nearest hundredth. 54. DEFG is a rhombus. Find EH. 55. DEFG is a rectangle. Find x and y. Round to the nearest hundredth. Homework 56. DEFG is a square. Find the length of each side. 57. DEFG is a rhombus. Find y. Geometry - Quadrilaterals ~9~ NJCTL.org
10 58. DEFG is a rectangle. Find DE. 59. PQRS is a rectangle. Find y. 60. DEFG is a square. Find y. 61. DEFG is a rhombus. Find y. 62. DEFG is rectangle. Find y. Round to the nearest hundredth. Geometry - Quadrilaterals ~10~ NJCTL.org
11 63. DEFG is square. Find DG. 64. DEFG is rhombus. Find x, y, and z. Trapezoids Classwork 65. RSTV is a trapezoid. Name the bases and legs. 66. Decide whether the quadrilateral is a trapezoid. Justify your answer. 67. HIJK is a trapezoid. Find m K and m J. Geometry - Quadrilaterals ~11~ NJCTL.org
12 68. HIJK is an isosceles trapezoid. Find x. 69. HIJK is an isosceles trapezoid. Find m H. 70. LM is the midsegment of trapezoid HIJK. Find LM. 71. LM is the midsegment of trapezoid HIJK. Find HI. 72. LM is the midsegment of trapezoid HIJK. Find x. Geometry - Quadrilaterals ~12~ NJCTL.org
13 Homework 73. EFGH is a trapezoid. Name the bases and legs. 74. Decide whether the quadrilateral is a trapezoid. Justify your answer. 75. QRST is a trapezoid. Find x. 76. QRST is an isosceles trapezoid. Find x. 77. QRST is an isosceles trapezoid. Find the length of the legs. 78. UV is the midsegment of trapezoid QRST is a trapezoid. Find TS. Geometry - Quadrilaterals ~13~ NJCTL.org
14 79. UV is the midsegment of trapezoid QRST is a trapezoid. Find UV. 80. UV is the midsegment of trapezoid QRST is a trapezoid. Find QR. Kites Classwork Decide whether the quadrilateral is a kite. Justify your answer The quadrilateral is a kite. Find x. 84. Geometry - Quadrilaterals ~14~ NJCTL.org
15 Homework Decide whether the quadrilateral is a kite. Justify your answer Geometry - Quadrilaterals ~15~ NJCTL.org
16 JKLM is a kite. Find x Geometry - Quadrilaterals ~16~ NJCTL.org
17 Family of Quadrilaterals Classwork 97. Define quadrilateral. Name the quadrilateral that always has the given property. 98. What is an equilateral quadrilateral? 99. Name the quadrilateral with perpendicular diagonals What quadrilateral has both pairs of opposite sides are congruent. In problems , identify the quadrilateral. (There may be more than one answer) Geometry - Quadrilaterals ~17~ NJCTL.org
18 Homework 105. Define a parallelogram. Name the quadrilateral that always has the given property The diagonals are congruent Has two pairs of congruent angles Exactly one pair of opposite sides are congruent. In problems , identify the quadrilateral. (There may be more than one answer) Coordinate Proofs Classwork 113. Given: E(-4,7), F(-3,2), G(-1,2), H(0,7) Prove: EFGH is an isosceles trapezoid 114. Given: P(3,4), Q(-3,4), R(3,-8), S(-3,-8) Prove: PQRS is a rectangle Geometry - Quadrilaterals ~18~ NJCTL.org
19 115. Given: A(-1,4), B(1,3) C(3,0), D(-1,2) Prove: ABCD is a trapezoid but not isosceles Homework 116. Given: J(-4,8), K(-1,11), L(2,8), M(-1,2) Prove: JKLM is a kite 117. Given: D(3,0), E(7,0), F(6,7), G(4,7) Prove: DEFG is an isosceles trapezoid 118. Given: P(3,5), Q(7,7), R(10,1), S(6,-1) Prove: PQRS is a parallelogram Proofs Classwork 119. Given: AMT HTM and HMT ATM Prove: MATH is a parallelogram 120. Given: COLD is a quadrilateral, m D=40 o, m O=140 o, and CO DL Prove: COLD is a isosceles trapezoid Homework 121. Given: DEFG is a rhombus and G is a right angle Prove: DEFG is a square Geometry - Quadrilaterals ~19~ NJCTL.org
20 122. Given: CDEF is a kite Prove: GE Unit Review Multiple Choice - Choose the correct answer for each question. No partial credit will be given. 1. Identify the polygon. a. octagon b. decagon c. dodecagon d. not a polygon 2. What is the sum of the measures of the interior angles of 24-gon? a b c d Use the parallelogram below for #'s Find the value of y. a. 16 b c. 9 d. 17 Geometry - Quadrilaterals ~20~ NJCTL.org
21 4. Find the m A. a. 98 o b. 82 o c. 72 o d. 108 o 5. EFGH is a rhombus. Find. FG a b c d IJKL is a kite. Find the m K. a. 13 b. 44 c d MNOP is a rectangle. Find NO. a. 5 b. 10 c d. 100 Geometry - Quadrilaterals ~21~ NJCTL.org
22 8. QRST is a trapezoid. If UV is the midsegment, find TS. a. 44 b c. 27 d ABCD is a trapezoid. Find m B. a. 62 b c d Which of the following statements is not true of a parallelogram? a. The opposite angles are congruent. b. The diagonals bisect each other. c. The opposite sides are congruent. d. The consecutive angles are congruent. Short Constructed Response - Write the answer for each question. No partial credit will be given. 11. Tell whether the quadrilateral is a parallelogram. If yes, state the appropriate theorem. Geometry - Quadrilaterals ~22~ NJCTL.org
23 12. Tell whether the quadrilateral is a parallelogram. If yes, state the appropriate theorem. 13. What is the measure of each interior angle of a regular 30-gon? 14. The measure of each angle of a regular convex polygon is Find the number of sides of the polygon. 15. QRST is a trapezoid. If UV is the midsegment, find x. Geometry - Quadrilaterals ~23~ NJCTL.org
24 Extended Constructed Response - Solve the problem, showing all work. Partial credit may be given. 16. ABCD is a parallelogram. Find the value of w, x, y, and z. 17. Given: ABCD is a quadrilateral and A(-2,0), B(0,4), C(5,4), D(8,0) Prove: ABCD is a trapezoid Geometry - Quadrilaterals ~24~ NJCTL.org
25 Answer Key 1. a. pentagon/concave/equilateral b. triangle/convex/regular c. not a polygon d. quadrilateral/convex/equiangular o o 4. m N = 60 o, m F = 158 o, m A = 116 o, m L = 84 o, m V = 165 o, m P = 137 o o o o sides 9. a. quadrilateral/convex/equiangular b. not a polygon c. hexagon/convex/regular d. decagon/concave/equilateral o o 12. m G = 126 o, m R = 120 o, m M = 163 o, m D = 170 o, m K = 124 o, m E = 117 o, m C = 152 o, m T = 108 o o o o sides 17. not a parallelogram 18. The figure is a parallelogram, because the diagonals bisect each other. 19. w=22, x=3, y=15, z= SR = m Q=107 o, m P=73 o 22. TR=5, PR= ST = x = 3 or The figure is a parallelogram, the opposite sides are congruent. 26. not a parallelogram 27. w=3.33, x=5, y=3, and z= m R=54 o, m P=54 o 29. SP = ST=TQ= PR = x = Yes, the diagonals of the quadrilateral bisect each other. 34. Yes, the opposite sides of the quadrilateral are congruent. 35. not a parallelogram 36. Yes, it is a parallelogram because it has 2 pairs of parallel sides 37. Yes, an angle of the quadrilateral is supplementary to its consecutive angles. 38. not a parallelogram 39. Yes, the opposite sides of the quadrilateral are congruent. 40. Yes, the opposite angles of the quadrilateral are congruent. 41. not a parallelogram Geometry - Quadrilaterals ~25~ NJCTL.org
26 42. Yes, one side of the quadrilateral is congruent and parallel. 43. not a parallelogram 44. Yes, the opposite sides of the quadrilateral are congruent. 45. sketches will vary 46. sketches will vary 47. x = x = x = DE=GF=27 and EF=DG= x = x = DG = EH = x = 25, y o 56. y = y = y = y = y = y = x=18, y=12, z=8 65. RS & VT are the bases. VR & TS are the legs 66. Yes. The consecutive interior angles are supplementary so, the bases are parallel. 67. m K=78 o, m J =36 o 68. x = x = LM = HI = x = EF & HG are the bases. EH & FG are the legs. 74. Yes. The quadrilateral has one pair of parallel sides 75. x = x = x = TS = UV = QR = not a kite 82. not a kite 83. Yes. The diagonals are perpendicular 84. x = x = x = x = x = Yes. The consecutive sides are congruent. 90. Yes. There is one pair of congruent opposite angles. 91. not a kite Geometry - Quadrilaterals ~26~ NJCTL.org
27 92. x = x = x = x = x = 22 o 97. A quadrilateral is a polygon with 4 sides. 98. A rhombus or a square. 99. A rhombus, square or a kite 100. A parallelogram, rectangle, rhombus, or a square 101. A parallelogram or rhombus 102. A rectangle or a square 103. A trapezoid 104. A kite 105. A parallelogram is quadrilateral where both pairs of opposite sides are parallel A rectangle, square, or isosceles trapezoid 107. A parallelogram, rectangle, square, rhombus, isosceles trapezoid, or kite A kite or isosceles trapezoid 109. An isosceles trapezoid 110. A rhombus, square, or kite 111. A parallelogram or rectangle 112. An isosceles trapezoid 113. EH FG, EF = HG, EF is not parallel to HG 114. QP=RS, QS=PR, QP RS, QS PR, and QS is perpendicular to QP 115. CD AB, AD is not congruent to BC 116. JK =KL, JM =ML 117. DE GF, DG =EF, DG is not parallel to EF 118. PQ SR, QR PS 119. Statements Reasons 1. <HTM; <ATM 1. Given 2. MA HT ; MH AT 2. Converse of alternate interior angles theorem 3. MATH is a parallelogram 3. Definition of parallelogram 120. Statements Reasons 1. m<d= 40, m<o=140, CO DL 1. Given 2. m<l = Consecutive interior angles are supplementary 3. Quad. COLD is an isosceles trapezoid 3. A trapezoid is isosceles if and only if base angles are congruent 121. Statements Reasons 1. DEFG is a rhombus; <G is a right angle 1. Given 2. m<g = Definition of right angles 3. m<d = Consecutive interior angles are supplementary 4. m<f = Consecutive interior angles are supplementary 5. m<e = Consecutive interior angles are supplementary 6. DEFG is a square 6. Definition of square Geometry - Quadrilaterals ~27~ NJCTL.org
28 122. Statements Reasons 1. CDEF is a kite 1. Given 2. FE 2. Definition of kite 3. FG 3. Reflexive property of congruence 4. CE ^ FD 4. Diagonals of a kite are perpendicular 5. <FGC and <FGE are right angles 5. Definition of perpendicular lines 6. DEGF 6. HL right triangle congruence theorem 7. GE 7. CPCTC Unit Review 1. C 2. B 3. C 4. A 5. A 6. D 7. B 8. C 9. A 10. D 11. Yes. Theorem Q9: If diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. 12. Yes. Theorem Q7: If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram degrees sides 15. x = w = 9, x = 3, y = 11, z = ABCD is a trapezoid, AD //BC and AB is not // to CD Geometry - Quadrilaterals ~28~ NJCTL.org
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