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Geometry Unit 9 Test - Quadrilaterals Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the values of the variables and the lengths of B the sides of this kite. x+ 5 | y–2 | 3x + 4 A B C D || || C x+ 6 x =8, y = 1; 1, 13 x = 1, y = 8; 6, 7 x = 1, y = 8; 1, 13 x =8, y = 1; 6, 6 2. Which statement is true? A All rectangles are squares. B All quadrilaterals are parallelograms. C All squares are quadrilaterals. D All quadrilaterals are squares. D 4. ABCD is a parallelogram. If then The diagram is not to scale. 3. Judging by appearances, which figure is a trapezoid? A A D A B C D B C 78 112 102 156 5. ABCD is a parallelogram. If then The diagram is not to scale. A B 37 D A B C D 101 C y° z° 73 132 122 58 x° A B C D 6. LMNO is a parallelogram. If NM = x + 23 and OL = 3x + 5 find the value of x and then find NM and OL. O 9. Find AM in the parallelogram if PN =10 and AO = 4. The diagram is not to scale. N M L A B C D M 7. For the parallelogram, if find scale. 3 A B C D A x = 9, NM = 32, OL = 32 x = 11, NM = 32, OL = 34 x = 11, NM = 34, OL = 34 x = 9, NM = 34, OL = 32 2 N and The diagram is not to P A B C D O 4 8 10 5 4 1 155 13 165 25 8. Find the values of the variables in the parallelogram. The diagram is not to scale. 10. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. A B 4x – 3 A B C D x = 9, y = 4 x = 4, y = 9 x = 9, y = 33 x = 9, y = 12 y+8 5y – 8 x + 24 D C 11. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain. A | | A Yes; two opposite sides are both parallel and congruent. B Yes; the diagonals are congruent. C No; you cannot prove that the quadrilateral is a parallelogram. D Yes; the diagonals bisect each other. 12. If find so that quadrilateral ABCD is a parallelogram. The diagram is not to scale. 3 B 1 | | 2 D A B C D 70 290 145 35 13. In the rhombus, C A B C D x = 30, y = 60, z = 3 x = 60, y = 150, z = 3 x = 30, y = 150, z = 6 x = 60, y = 60, z = 6 14. DEFG is a rectangle. DF = 5x – 3 and EG = x + 37. Find the value of x and the length of each diagonal. A x = 5, DF = 42, EG = 42 B x = 10, DF = 42, EG = 42 C x = 10, DF = 47, EG = 47 D x = 10, DF = 47, EG = 51 Find the value of each variable. The diagram is not to scale. 15. Which description does NOT guarantee that a quadrilateral is a rectangle? A a quadrilateral with all four angles right B a quadrilateral with diagonals that are congruent and bisect each other C a quadrilateral with all congruent angles D a parallelogram with congruent sides 16. Find the values of a and b.The diagram is not to A 79°; 158° scale. B 22°; 158° C 79°; 101° D 22°; 101° 131° 18. Find to scale. A b° 1 | 41° in the kite. The diagram is not 3 D 28° 2 || C A B C D 28, 28 28, 62 62, 62 62, 28 19. Which description does NOT guarantee that a trapezoid is isoscles? A congruent bases B congruent legs C congruent diagonals D both pairs of base angles congruent 20. are base angles of isosceles trapezoid JKLM. If and 21. | 5 84 48 96 and diagram is not to scale. U S Find The || || A B C D R | 17. The isosceles trapezoid is part of an isosceles triangle with a 22° vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not to scale. B || A B C D | a° T A B C D 20 70 10 100 Geometry Unit 9 Test - Quadrilaterals Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: B C A C D A A B A A D C A C D A C B A D A