Honors Geometry hapter 6 upplement Name: 1. Given: Q m Q = (4x) m Q = (5x) m Q = 40 m Q = 32 Find the value of x, m Q, m Q, m Q Q (4x) (5x) 40 32 2. Given: m = (8x + 20) m = (150 6x) m = (12x + 60) a) Find the value of x and m. b) Is? 3. Given: parallelogram m = (2x + y) m = (3x + 5y) m = (4x 3y + 8) Find the values of x, y, m, and m. 4. Given: F is a rectangle m = (6x + 3y) m F = (10x + 15y) Find the values of x and y. F 5. Given: is a rhombus m = (x 2 ) m = (6x + 40) Fimd m. 6. Given: QF is a trapezoid FQ m = (3x 2 ) m Q = (3x) m F = (12x) Find m. F Q
7. Y is equilateral and has a perimeter of 72. Find the perimeter of parallelogram. Y 8. he angles of a rhombus are 60 and 120. he short diagonal is 8 cm. Find the perimeter of the rhombus. 9. Fill in the table: roperty arallelogram ectangle hombus quare Kite rapezoid Isosceles rapezoid oth pair opposite sides parallel Exactly 1 pair opposite sides parallel iagonals perpendicular iagonals congruent iagonals bisect each other oth pairs opposite sides congruent Exactly 1 pair of opposite sides congruent ll sides congruent oth pair opposite angles congruent Exactly 1 pair opposite angles congruent ll angles congruent oth pair of opposite angles supplementary t least one right angle
10. Given: W is a kite = x + 5 = y + 9 W = 2y +7 W = 3x 10 Find the perimeter of the kite W 11. Given trapezoid with m = (12x) m = (300 22x) m = (x 2 ) etermine m. (x 2 ) (300 22x) (12x) For numbers 12 17, write for always, for sometimes, or N for never. 12. If two lines are cut by a transversal, alternate exterior angles are congruent. 13. If two parallel lines are cut by a transversal, corresponding angles are congruent. 14. he diagonals of a kite bisect each other. 15. he diagonals of a parallelogram bisect each other. 16. he diagonals of a rectangle are congruent. 17. he diagonals of an isosceles trapezoid bisect each other. 18. Find the perimeter of a) the isosceles trapezoid. x + 5 (9x + 92) (32x) b) parallelogram. x x x + 10 (2x + 50) 3x (4x) 19. pair of consecutive angles in a rhombus have measures in the ratio of 7 to 5. Find the measure of the smallest angle. 20. One upper base angle and one lower base angle in an isosceles trapezoid are in the ratio of 2 to 7. Find the measure of the largest angle.
21. is a kite. Y = 4x Y = x + 7.5 = 10x + 3 = 5x 4 Find the perimeter. Y 22. List all the possible quadrilateral that satisfy the following statements. hoose from: quadrilateral (Q), parallelogram (), ectangle (c), hombus (h), quare (), Kite (K), rapezoid (), Isosceles rapezoid (I) a) I am a quadrilateral with congruent diagonals. b) I am a parallelogram with perpendicular diagonals. c) I am a quadrilateral with diagonals bisected. d) I am a quadrilateral with two unique pairs of congruent, consecutive sides. e) I am a parallelogram with congruent, perpendicular diagonals. f) I am a quadrilateral with one pair of opposite sides parallel. g) I am a quadrilateral with diagonals perpendicular and bisectors of each other. h) I am a parallelogram with two opposite angles bisected by a diagonal. i) I am a parallelogram with a right angle. j) I am a rectangle with perpendicular diagonals. 23. In parallelogram, = 9y + 10, = 6y + 40, = 1 y 50. Find,,, and. 2 E 24. In parallelogram, m = x and m = (2x + 60). Find the measure of angle. For numbers 25 38, answer rue or False. 25. parallelogram is a rectangle. 26. kite is a quadrilateral. 27. n isosceles trapezoid has two congruent legs. 28. trapezoid has two pairs of opposite sides parallel. 29. square is kite. 30. If one of the angles of a parallelogram is a right angle, the parallelogram is a square. 31. rhombus is a square. 32. iagonals of a rectangle are congruent. 33. iagonals of a rhombus are congruent. 34. If two parallel lines are cut by a transversal, interior angles on the same side of the transversal are congruent. 35. he diagonals of an isosceles trapezoid bisect each other.
36. In a kite, the diagonals are the perpendicular bisectors of each other. 37. rectangle is a trapezoid. 38. iagonals of parallelogram are congruent. For numbers 39 44, write for always, for sometimes, or N for never. 39. rhombus is a square. 40. square is a rectangle 41. trapezoid is a parallelogram. 42. parallelogram is a quadrilateral. 43. he diagonals of an isosceles trapezoid are perpendicular. 44. square is a rhombus. 45. In rectangle EFGH, m FEG = (4x + 5) and m GEH = (5x 14). Find m GEH. E F J 46. In rectangle EFGH, EJ = 2x + 3 and FJ = 12 x. Find FH. H G 47. In square JKL, m KJL = (9x). Find the value x. J K 48. In square JKL, JK = x 2 15 and KL = 2x. Find the perimeter of the square. L 49. In rhombus, m E = (x), m E = (3x). Find the m. E 50. In rhombus, = 3x + 4, = 7x 20. Find the perimeter. 51. Find the perimeter of Q if Q is a kite. 5x 1 Q 3x x + 4 8x + 3 52. pair of consecutive angles of a parallelogram have measures in the ratio of 5 to 4. Find the measure of the larger angle.
53. is an isosceles trapezoid. Find if: = x + 5, = 2x + 8 and = 2x + 17.