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Name:_______________________ Geometry Chapter 6 Test B per:_____________ Date:____________________ Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. The isosceles trapezoid is part of an isosceles triangle with a 56° 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. a. 56°; 124° ____ ____ b. 56°; 118° 2. In quadrilateral MNOP, MNOP be? (Draw a picture) a. parallelogram or rhombus b. parallelogram only 53° Which of a parallelogram, trapezoid, or rhombus could quadrilateral c. trapezoid only d. any of the three 106° b° a. b. 4. a. 141 ____ d. 62°; 118° 3. Find the values of a and b.The diagram is not to scale. a° ____ c. 62°; 124° c. d. are base angles of isosceles trapezoid JKLM. If (Draw a picture) b. 70.5 c. 39 5. Which statement is true? a. All rectangles are parallelograms. b. All quadrilaterals are squares. c. All quadrilaterals are rectangles. d. All parallelograms are rectangles. and d. 2 ____ 6. Which description does NOT guarantee that a trapezoid is isosceles? a. congruent bases b. congruent diagonals c. both pairs of base angles congruent d. congruent legs ____ 7. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. A B 2x – 0 y + 32 6y – 8 x+ 2 D C a. x = 2, y = 40 ____ b. x = 2, y = 4 c. x = 2, y = 8 8. If and be a parallelogram. The diagram is not to scale. O M c. 1 3 b. x = 4, y = 3 ____ find the values of x and y for which LMNO must N L a. d. x = 8, y = 2 1 3 d. x = 11, y = 3 x = 4, y = x = 11, y = 9. DEFG is a rectangle. DF = 2x – 6 and EG = x + –4. Find the value of x and the length of each diagonal. a. x = 2, DF = –2, EG = –2 c. x = 1, DF = –3, EG = –3 b. x = 2, DF = –3, EG = –3 d. x = 2, DF = –2, EG = 2 ____ 10. For the parallelogram, if 3 2 a. 16 and find The diagram is not to scale. 4 1 b. 162 c. 172 d. 18 Short Answer 11. In the rhombus, not to scale. Find the value of each variable. The diagram is | | 11. y = ________________ 3 x = ________________ 1 z = _________________ | | 2 12. ABCD is a parallelogram. If A then B D The diagram is not to scale. 12. mBCD ___________ C 13. Find the coordinates of the midpoint of the segment with the given endpoints. P( 2, -1) and Q( 5, 3) 13. __________________ 14. Find in the kite. The diagram is not to scale. | A 3 | 1 m3 ______________ 2 B || || D 32° 14. m1 ______________ C 15. ABCD is a parallelogram. If A then The diagram is not to scale. B 15. mCDA ___________ D C 16. Isosceles trapezoid ABCD has legs find the value of y. (Draw a picture) and and base If AB = 6y – 4, BC = 2y – 5, and CD = 7y – 13, 16. y = _______________ 17. Find AM in the parallelogram if PN =15 and AO = 5. The diagram is not to scale. M N 17. AM _______________ A P O 18. Complete this statement: For parallelogram ABCD, Then state a definition or theorem that justifies your answer. D C 18. BO _______________ _______________________ O A B 19. Find the values of the variables in the parallelogram. The diagram is not to scale. 29 19. x = ________________ 100 y =_________________ z =_________________ y° z° x° 20.Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale. 10x 20. y = _______________ x = _______________ x + 17 3y length short side_________ length long side__________ y + 62 21. One side of a kite is 6 cm less than four times the length of another side. The perimeter of the kite is 68 cm. Find the lengths of the sides of the kite. (Draw a Picture) 21. length short sides ______________ length long sides _______________ 22. Find the values of the variables and the lengths of the sides of this kite. y–5 | x+ 2 22. y = ________________ | x = ________________ || || length long side__________ 3x + 5 x+ 7 length short side_________ 23. Give the name that best describes the parallelogram and find the measures of the numbered angles. The diagram is not to scale. 23. ___________________ | m1 __________ 4 | | 3 1 2 | m2 __________ m3 __________ m4 __________ 24. and Find The diagram is not to scale. 24. R =______________ | | S || || U T 25. Find the length of the segment to the nearest 10th. 27. TR = _____________5 EXTRA CREDIT 26. Use the given endpoint R and midpoint M of RS to find the coordinates of the other endpoint S. (1 point) 26. _______________________ R( -3, 7), M( 2, -4) 27. Write a proof (3 points) Given: Prove: VX = XT V Statements U X S T Reasons