Geometry - Chapter 6 Review
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1 Class: Date: Geometry - Chapter 6 Review 1. Find the sum of the measures of the angles of the figure. 4. Find the value of x. The diagram is not to scale. A B. 900 C. 540 D The sum of the angle measures of a polygon with s sides is Find s. A. 13 B. 14 C. 17 D. 15 A. 90 B. 45 C. 35 D Find m A. The diagram is not to scale. 3. What is the measure of one angle in a regular 30-gon? A. 192 B. 84 C. 168 D A. 107 B. 117 C. 63 D The sum of the measures of two exterior angles of a triangle is 264. What is the measure of the third exterior angle? A. 96 B. 84 C. 106 D. 86 1
2 7. How many sides does a regular polygon have if each exterior angle measures 30? A. 15 sides B. 12 sides C. 14 sides D. 11 sides 10. Find the values of the variables in the parallelogram. The diagram is not to scale. 8. This jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to fill its four corners. Find the measure of the foam angle marked. A. x 53, y 31, z 96 B. x 53, y 53, z 127 C. x 31, y 53, z 96 D. x 31, y 53, z 127 A. 54 B. 36 C. 18 D A nonregular hexagon has five exterior angle measures of 55, 58, 69, 57, and 55. What is the measure of the interior angle adjacent to the sixth exterior angle? A. 104 B. 66 C. 114 D In the parallelogram, m QRP 32 and m PRS 84. Find m PQR. The diagram is not to scale. A. 84 B. 116 C. 32 D. 64 2
3 12. ABCD is a parallelogram. If m CDA 63, then m ABC?. The diagram is not to scale. A. 117 B. 127 C. 78 D What is the missing reason in the proof? Given: ABCD with diagonal BD Prove: ABD CDB Statements Reasons 1. AD BC 1. Definition of parallelogram 2. ADB CBD 2. Alternate Interior Angles Theorem 3. AB CD 3. Definition of parallelogram 4. ABD CDB 4. Alternate Interior Angles Theorem 5. DB DB 5.? 6. ABD CDB 6. ASA A. Reflexive Property of Congruence C. ASA B. Alternate Interior Angles Theorem D. Definition of parallelogram 3
4 14. In parallelogram DEFG, DH = x + 2, HF = 2y, GH = 4x 3, and HE = 5y + 1. Find the values of x and y. The diagram is not to scale. 16. In the figure, the horizontal lines are parallel and AB BC CD. Find JM. The diagram is not to scale. A. x = 8, y = 5 B. x = 5, y = 8 C. x = 4, y = 6 D. x = 6, y = Find AM in the parallelogram if PN =15 and AO = 6. The diagram is not to scale. A. 27 B. 36 C. 9 D If m B m D 46, find m C so that quadrilateral ABCD is a parallelogram. The diagram is not to scale. A. 12 B. 6 C. 15 D. 7.5 A. 46 B. 92 C. 134 D
5 18. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. 19. Which statement can you use to conclude that quadrilateral XYZW is a parallelogram? A. x = 8, y = 6 B. x = 6, y = 8 C. x = 8, y = 17 D. x = 8, y = 10 A. YN NX and XN NY B. XW WZ and XY WZ C. XW YZ and XY WZ D. XW YZ and XY YZ 20. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given: XN NZ and NY NW A. Yes; opposite sides are congruent. B. Yes; two opposite sides are both parallel and congruent. C. Yes; diagonals of a parallelogram bisect each other. D. No; you cannot determine that the quadrilateral is a parallelogram. 5
6 21. Classify the figure in as many ways as possible. 23. In the rhombus, m What are m 2 and m 3? The diagram is not to scale. A. rectangle, square, quadrilateral, parallelogram, rhombus B. rectangle, square, parallelogram C. rhombus, quadrilateral, square D. square, rectangle, quadrilateral 22. In the rhombus, m 1 15x, m 2 x y, and m 3 30z. Find the value of each variable. The diagram is not to scale. A. m 2 = 40, m 3 70 B. m 2 = 140, m 3 20 C. m 2 = 40, m 3 20 D. m 2 = 140, m Find the measure of the numbered angles in the rhombus. The diagram is not to scale. A. x = 12, y = 84, z = 6 B. x = 12, y = 174, z = 3 C. x = 6, y = 84, z = 3 D. x = 6, y = 174, z = 6 A. m 1 90, m 2 = 24, and m 3 78 B. m 1 90, m 2 = 66, and m 3 24 C. m 1 90, m 2 = 24, and m 3 24 D. m 1 90, m 2 = 24, and m DEFG is a rectangle. DF = 5x 3 and EG = x + 5. Find the value of x and the length of each diagonal. A. x = 1, DF = 6, EG = 6 B. x = 2, DF = 7, EG = 12 C. x = 2, DF = 6, EG = 6 D. x = 2, DF = 7, EG = 7 6
7 26. In rectangle KLMN, KM = 10x 24 and LN = 64. Find the value of x. 28. Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain. A. 5 B. 4 C. 3 D In rectangle PQRS, PR = 18x 28 and QS = x Find the value of x and the length of each diagonal. A. Parallelogram ABCD is a rhombus, because the diagonal bisects two angles. B. Parallelogram ABCD is a rectangle, because the diagonal creates congruent angles. C. Parallelogram ABCD is a square, because all four angles have the same measure. D. There is not enough information. 29. In quadrilateral ABCD, m ACD 2x 4 and m ACB 5x 8. For what value of x is ABCD a rhombus? A. x = 24, PR = 202, QS = 202 B. x = 12, PR = 392, QS = 392 C. x = 24, PR = 404, QS = 404 D. x = 25, PR = 422, QS = 422 A. 3 B. 4 C. 5 D. 6 7
8 30. In quadrilateral ABCD, AE x 6 and BE 3x 18. For what value of x is ABCD a rectangle? 33. The isosceles trapezoid is part of an isosceles triangle with a 42 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. 18 B. 12 C. 16 D Find the values of a and b. The diagram is not to scale. A. 69 ; 138 B. 42 ; 111 C. 42 ; 138 D. 69 ; LM is the midsegment of ABCD. AB 72 and DC 104. What is LM? A. a 115, b 71 B. a 115, b 65 C. a 109, b 71 D. a 109, b J and M are base angles of isosceles trapezoid JKLM. If m J 18x 8, and m M 11x 15, find m K. A. 1 B. 154 C. 77 D. 26 A. 176 B. 98 C. 88 D. 32 8
9 35. LM is the midsegment of ABCD. AB x 8, LM 4x 3, and DC 243. What is the value of x? 37. m R 120 and m S 110. Find m T. The diagram is not to scale. A. 43 B. 35 C. 286 D Find m 1 and m 3 in the kite. The diagram is not to scale. A. 60 B. 10 C. 110 D Find the values of the variables and the lengths of the sides of this kite. A. m 1 17, m 3 73 B. m 1 17, m 3 17 C. m 1 73, m 3 17 D. m 1 73, m 3 73 A. x = 9, y = 14; 11, 20 B. x = 14, y = 9; 11, 11 C. x = 14, y = 9; 6, 16 D. x = 9, y = 14; 6, Which diagram shows the most useful positioning and accurate labeling of an isosceles trapezoid in the coordinate plane? 9
10 A. 40. Which diagram shows the most useful positioning of a rectangle in the first quadrant of a coordinate plane? A. B. B. C. C. D. D. 10
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