Geometry Tutor Worksheet 9 Quadrilaterals 1
Geometry Tutor - Worksheet 9 - Quadrilaterals 1. Which name best describes quadrilateral DEFG? 2. Which name best describes quadrilateral ABCD? 3. Which name best describes quadrilateral QRST? 2
4. Which name best describes quadrilateral WXYZ? 5. Which name best describes quadrilateral MNOP? 6. Which name best describes quadrilateral HJKL? 3
7. Quadrilateral ABCD is a parallelogram. What are the lengths of sides AD and CD and the measures of C and D? 8. Quadrilateral WXYZ is a trapezoid. What is the length of side XY and what are the measures of W, Y, and Z? 4
9. Given quadrilateral DEFG is a kite. What are the lengths of sides DG and FG and the measures of E and G? 10. Quadrilateral FGHJ is a rhombus. What are the lengths of sides GH, HJ, and JF and the measures of H and J? 5
11. Given quadrilateral ABCD is a trapezoid. What are the measures of A and D? 12. Given quadrilateral DEFG. What is the measure of F? 6
13. What is the best name for quadrilateral WXYZ? 14. Quadrilateral QRST is a parallelogram. What is the measure of S? 7
15. Quadrilateral VWXY is a parallelogram. What is the measure of WYX? 16. Quadrilateral JKLM is a parallelogram, MK = 12, and YL = 9. What are the lengths of MY, KY, JY, and JL? 8
17. Quadrilateral BCDE is a parallelogram. What are the measures of BDC and BCD? 18. Quadrilateral WXYZ is a parallelogram. What is the value of x and what is the measure of W? 9
19. Quadrilateral UVWX is a parallelogram. What is the value of x and what are the measures of X and W? 20. Quadrilateral RSTU is a parallelogram. What is the value of x and what are the lengths of RS, and TU? 10
21. Quadrilateral JKLM is a parallelogram. What is the value of x and what are the measures of J and M? 22. Quadrilateral JKLM is a rectangle, MU = 3x + 6, and JU = 4x 4. What is the value of x and what is the length of MK? 11
23. Quadrilateral DEFG is a parallelogram. What is the value of x and what are the measures of D and E? 24. Quadrilateral RSTU is a parallelogram, m RSU = 2x + 14 and m TSU = 2x 7. What is the value of x? 12
25. Quadrilateral STUV is a parallelogram, TE = 8 + 4x, and EV = 8x 8. What is the value of x? 13
Answers - Geometry Tutor - Worksheet 9 - Quadrilaterals 1. Which name best describes quadrilateral DEFG? Quadrilateral DEFG has four right angles, but all sides are not congruent. Thus, it is a rectangle. Answer: rectangle 2. Which name best describes quadrilateral ABCD? Quadrilateral ABCD has four congruent sides, but the angles are not congruent. Thus, it is a rhombus. Answer: rhombus 3. Which name best describes quadrilateral QRST? 14
Quadrilateral QRST has two pairs of consecutive congruent sides. Thus, it is a kite. Answer: kite 4. Which name best describes quadrilateral WXYZ? Quadrilateral WXYZ has exactly one pair of parallel sides. Thus, it is a trapezoid. Answer: trapezoid 5. Which name best describes quadrilateral MNOP? 15
Quadrilateral MNOP has four right angles and four congruent sides. Thus, it is a square. Answer: square 6. Which name best describes quadrilateral HJKL? Quadrilateral HJKL has two pairs of opposite parallel sides. Thus, it is a parallelogram. Answer: parallelogram 7. Quadrilateral ABCD is a parallelogram. 16
What are the lengths of sides AD and CD and the measures of C and D? Since quadrilateral ABCD is a parallelogram, opposite angles are congruent and opposite side are congruent. Answer: AD = 8, CD = 15, m C = 97, and m D = 83 8. Quadrilateral WXYZ is a trapezoid. What is the length of side XY and what are the measures of W, Y, and Z? Since quadrilateral WXYZ is a trapezoid, the figure contains exactly one pair of parallel sides. Thus the angled sides are both transversals cutting two parallel lines and adjacent angles on each side of the trapezoid are supplementary because they are same side interior angles. Furthermore, since the base angles, Y and Z, are shown to be congruent, the figure is an isosceles trapezoid, so the slanted sides have the same length. Answer: XY = 9, m W = 106, m Y = 74, and m Z = 74 17
9. Given quadrilateral DEFG is a kite. What are the lengths of sides DG and FG and the measures of E and G? The properties of kites include two pairs of consecutive congruent sides and exactly one pair of congruent opposite angles. Thus, m E = m G. Since the figure is a quadrilateral, the sum of the interior angles is 360, so 60 + 80 + 2x = 360; 140 + 2x = 360; 2x = 220; x = 110 Answer: DG = 14, FG = 11, m E = 110, and m G = 110 10. Quadrilateral FGHJ is a rhombus. What are the lengths of sides GH, HJ, and JF and the measures of H and J? Since the figure is a rhombus, all sides have the same length and opposite angles have the same measure. Answer: GH = 12.9, HJ = 12.9, JF = 12.9, m H = 104. and m J = 76 18
11. Given quadrilateral ABCD is a trapezoid. What are the measures of A and D? Since quadrilateral WXYZ is a trapezoid, the figure contains exactly one pair of parallel sides. Thus the angled sides are both transversals cutting two parallel lines. Thus, adjacent angles on each side of the trapezoid are supplementary because they are same side interior angles. Answer: m A = 60 and m D = 85 12. Given quadrilateral DEFG. What is the measure of F? The sum of the interior angles of a quadrilateral is 360, so 65 + 110 + 87 + m F = 360; 262 + m F = 360; m F = 98 Answer: 98 19
13. What is the best name for quadrilateral WXYZ? The figure shows congruent base angles in both the top and the bottom of the quadrilateral so it s isosceles. Furthermore, the figure has exactly one set of parallel sides, so it s a trapezoid. Answer: isosceles trapezoid 14. Quadrilateral QRST is a parallelogram. What is the measure of S? In a parallelogram, opposite angles are congruent to each other. Answer: 135 20
15. Quadrilateral VWXY is a parallelogram. What is the measure of WYX? In a parallelogram, adjacent angles are supplementary, so 60 + (52 + m WYX) = 180; 112 + m WYX = 180; m WYX = 68 Answer: 68 16. Quadrilateral JKLM is a parallelogram, MK = 12, and YL = 9. What are the lengths of MY, KY, JY, and JL? In a parallelogram, the diagonals bisect each other. Thus, MY KY and LY YJ. Therefore, MY + KY = 2MY = 2 KY = 12, so MY = KY = 6, and YL = JY = 9, so 2YL = 2JY = 18. Answer: MY = 6, KY = 6, JY = 9, and JL = 18 21
17. Quadrilateral BCDE is a parallelogram. What are the measures of BDC and BCD? In a parallelogram, opposite angles are congruent and adjacent angles are supplementary, so 55 + (62 + m BDC) = 180; 117 + m BDC = 180; m BDC = 63 Answer: m BDC = 63, m BCD = 55 18. Quadrilateral WXYZ is a parallelogram. What is the value of x and what is the measure of W? In a parallelogram, opposite angles are congruent and adjacent angles are supplementary, so 80 + (11x 10) = 180; 70 + 11x = 180; 11x = 110; x = 10 Then 11(10) 10 = 110 10 = 100 Answer: x = 10, m W = 100 22
19. Quadrilateral UVWX is a parallelogram. What is the value of x and what are the measures of X and W? In a parallelogram, adjacent angles are supplementary, so (6x + 15) + (9x + 15) = 180; 15x + 30 = 180; 15x = 150; x = 10 Then 6(10) + 15 = 75, and 9(10) + 15 = 105. Answer: m X = 75, m W = 105 20. Quadrilateral RSTU is a parallelogram. What is the value of x and what are the lengths of RS, and TU? In a parallelogram opposite sides are congruent, so 2x + 15 = x + 15; x = 0. Then, RS = 0 + 15 = 15 and TU = 2(0) + 15 = 15. Answer: x = 0, RS = 15, TU = 15 23
21. Quadrilateral JKLM is a parallelogram. What is the value of x and what are the measures of J and M? In a parallelogram, adjacent angles are supplementary, so (13x) + (5x) = 180; 18x = 180; x = 10 Then 13(10) = 130, and 5(10) = 50. Answer: m J = 130, m M = 50 22. Quadrilateral JKLM is a rectangle, MU = 3x + 6, and JU = 4x 4. What is the value of x and what is the length of MK? In a rectangle, the diagonals are congruent and bisect each other. Thus, MU KU JU LU, so MU = JU; 3x + 6 = 4x 4; x = 10 Then MU = 3(10) + 6 = 36 and MK = 2MU = 2(36) = 72. Answer: x = 10, MK = 72 24
23. Quadrilateral DEFG is a parallelogram. What is the value of x and what are the measures of D and E? In a parallelogram, adjacent angles are supplementary and opposite angles are congruent, so 3x + 11 = 5x 9; 2x = 20; x = 10 and m E = 5(10) 9 = 41. Answer: m D = 139 and m E = 41 24. Quadrilateral RSTU is a parallelogram, m RSU = 2x + 14 and m TSU = 2x 7. What is the value of x? In a parallelogram, adjacent angles are supplementary, so 125 + (2x + 14) + (2x 7) = 180 125 + 4x + 7 = 180 132 + 4x = 180 4x = 48 x = 12 Answer: 12 25
25. Quadrilateral STUV is a parallelogram, TE = 8 + 4x, and EV = 8x 8. What is the value of x? In a parallelogram, the diagonals bisect each other, so TE EV and TE = EV, so 8 + 4x = 8x 8; 4x = 16; x = 4 Answer: 4 26