Name: Date: 1. In the accompanying diagram of rhombus ACD, the lengths of the sides A and C are represented by 3x 4 and 2x + 1, respectively. Find the value of x. 4. In the accompanying figure, ACD is a parallelogram, m A = 2x + 35, and m C = 5x 22. Find the value of x. 2. In the accompanying diagram of parallelogram ACD, m A = 2x 10 and m = 5x + 15. Find x. 5. In the accompanying diagram of rhombus ACD, the lengths of sides A and C are represented by 3x 8 and 2x + 1, respectively. Find the value of x. 3. In the parallelogram ACD, m A = 2x + 50 and m C = 3x + 40. The measure of A is A. 18. 20 C. 70 D. 86 6. The perimeter of a square is 20x 4. Which expression represents a side of the square in terms of x? A. 5x. 10x 2 C. 8x 16 D. 5x 1 page 1
7. In the accompanying diagram of rectangle ACD, diagonal AC = 8x + 4 and diagonal D = 5x + 16. Find the value of x. 11. In the accompanying diagram of parallelogram ACD, diagonals AC and intersect D at E, E = 2x and ED = x 10. What is the value of x? A. 30. 30 C. 6 D. 6 8. In the accompanying diagram, ACD is a parallelogram with m = 120, m C = 60, m D = 2x + 5y, and m A = 4x + y. Find the values of x and y. Check your solution. 12. In the diagram below of isosceles trapezoid DEFG, DE GF, DE = 4x 2, EF = 3x + 2, FG = 5x 3, and GD = 2x + 5. Find the value of x. 9. The diagonals of rectangle ACD intersect at E. If DE = 3x + 1 and AC = 5x + 4, find the value of x. 10. If the measures of two opposite angles of an isosceles trapezoid are 2x + 20 and 3x, what is the value of x? page 2
13. In the diagram below of quadrilateral ACD with diagonal D, m A = 93, m AD = 43, m C = 3x + 5, m DC = x + 19, and m DC = 2x + 6. Determine if A is parallel to DC. Explain your reasoning. 16. In rectangle MATH, AT = 8 and TH = 12. Find the length of diagonal HA to the nearest tenth. 17. The perimeter of a rhombus is 60. If the length of its longer diagonal measures 24, the length of the shorter diagonal is A. 9. 15 C. 18 D. 20 14. What is the length of a diagonal of a rectangle whose sides are 3 and 7? 18. In the diagram below, LATE is an isosceles trapezoid with LE = AT, LA = 24, ET = 40, and AT = 10. Altitudes LF and AG are drawn. 15. The diagonals of a rhombus are 10 centimeters and 24 centimeters. A side of the rhombus measures A. 10 cm. 13 cm C. 24 cm D. 26 cm What is the length of LF? A. 6. 8 C. 3 D. 4 page 3
19. In rhombus ACD, with diagonals AC and D, AD = 10. 21. In the accompanying diagram of rhombus RUDE, m RUE = 21 and UE = 20. Find, to the nearest tenth, the a) length of RD b) perimeter of RUDE If the length of diagonal AC is 12, what is the length of D? A. 8. 16 C. 44 D. 136 22. In the accompanying diagram, STAR is an isosceles trapezoid with SR = TA, ST = 20, RA = 30, m SRA = 40, and altitudes SE and TF are drawn a) Find SE to the nearest tenth. 20. In the accompanying diagram of rhombus ACD, m AD = 36 and the length of diagonal AEC = 16. b) Find SR to the nearest tenth. c) Find the perimeter of trapezoid STAR to the nearest integer. d) Find the area of trapezoid STAR to the nearest integer. a) Find the length of diagonal D to the nearest tenth. b) Find the perimeter of rhombus ACD to the nearest integer. page 4
23. In the diagram below, quadrilateral STAR is a rhombus with diagonals SA and TR intersecting at E. ST = 3x + 30, SR = 8x 5, SE = 3z, TE = 5z + 5, AE = 4z 8, m RTA = 5y 2, and m TAS = 9y + 8. Find SR, RT, and m TAS. 25. In isosceles trapezoid ACD, m D = 70, A = 6, and DC = 14. a) Find DE. b) Find the altitude AE to the nearest integer. c) Using the answer to part b, find the area of trapezoid ACD. d) Find AD to the nearest integer. 24. In the accompanying diagram, square ADFE is inscribed in rectangle ACD, E : A = 3 : 7, and the perimeter of ACD is 132. 26. In the accompanying diagram, diagonals TA and EM of rhombus TEAM intersect at point S. The length of diagonal TA is 30 and anglemsam = 53. Find: a) the length of AE b) the area of rectangle ACD c) the ratio of the area of rectangle ECF to the area of rectangle ACD, in simplest form a) Find the length of side MA to the nearest integer. b) Find the length of diagonal EM to the nearest integer. c) Find the perimeter of EMA to the nearest integer. page 5
27. In the accompanying diagram of rhombus ACD, diagonal AC = 80 and m AC = 36. 30. In the accompanying diagram of rhombus QRST, diagonals QS and RT intersect at M. Which statement must be true? a) Find the length of a side of the rhombus to the nearest tenth. b) Using your answer in part a, find the perimeter of rhombus ACD. c) Find the length of diagonal to the nearest integer. A. Triangle QRM is an isosceles right triangle.. QRM = SRM C. Triangle QRM is an obtuse triangle. D. QS = RT 28. Which property is not true for all parallelograms? A. Opposite angles are congruent.. Consecutive angles are supplementary. C. Opposite sides are congruent. 31. If quadrilateral ACD is a parallelogram, which statement must be true? D. Diagonals are congruent. 29. A quadrilateral has diagonals that are congruent but not perpendicular. The quadrilateral contains no right angles. The quadrilateral could be A. a square. an isosceles trapezoid C. a rectangle D. a rhombus A.. C. D. AC D AC = D AC bisects DA and CD. AC and D bisect each other. page 6
32. In the diagram below, parallelogram ACD has diagonals AC and D that intersect at point E. 33. The length of a rectangle is 3 inches more than its width. The area of the rectangle is 40 square inches. What is the length, in inches, of the rectangle? A. 5. 8 C. 8.5 D. 11.5 Which expression is not always true? A. DAE = CE. DEC = EA C. AC = D D. DE = E 34. In rhombus ACD, the diagonals AC and D intersect at E. If AE = 5 and E = 12, what is the length of A? A. 7. 10 C. 13 D. 17 35. The diagonals of a rhombus have lengths of 16 and 30. The length of a side of the rhombus is A. 17. 15 2 C. 16 2 D. 34 page 7
Problem-Attic format version 4.4.239 c 2011 2015 EducAide Software Licensed for use by scott hendrie Terms of Use at www.problem-attic.com 02/10/2016 1. 5 2. 25 3. C 4. 19 5. 9 6. D 7. 4 8. (10, 20) 9. 2 10. 32 11. 12. 3 13. 14. 15. Parallel 58 16. 14.4 17. 18. 19. C A 20. 5.2; 34 21. 7.7; 42.8 22. 4.2; 6.5; 63; 105 23. SR = 51, RT = 90, m TAS = 62 24. 24; 1,008; 3 : 7 25. 4; 11; 110; 12 26. 25; 40; 90 27. 49.4; 197.6; 58 28. 29. 30. 31. 32. 33. 34. 35. D D C C A