Geometry Chapter 6 Review

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1. Find the sum of the measures of the interior angles of a convex 30-gon. 5040 5400 360 168 30

2. Find the measure of one interior angle of a convex decagon. 80 180 1440 144 360

3. Find the sum of the measures of the exterior angles of a convex 21-gon. 210 21 180 3420 360

4. If the measure of each interior angle of a regular polygon is 108, find the number of sides in the figure. 72 5 9 15 108

5. Find x for parallelogram ABCD if BC = 3x + 20 and AD = 5x – 12. 16 4 10.25 21.5 5

6. Parallelogram ABCD has vertices A(0,0), B (2,4) and C(10,4) 6. Parallelogram ABCD has vertices A(0,0), B (2,4) and C(10,4). Find the possible coordinates of D. (8,0) (10,0) (0,4) (10,8) (0, 8)

7. ABCD is a rectangle with diagonals AC and BD 7. ABCD is a rectangle with diagonals AC and BD. If AC = 2x + 10 and BD = 56, find x. 18 33 78 122 23

8. Find the median of a trapezoid with bases of 15 m and 27 m. 6 12 21 19 24

9. The length of one base of a trapezoid is 44, the median is 36 and the other base is 2x + 10. Find x. 17 9 21 40 35

10. Find x. X-20 x 138 2x + 10 X + 40 30 102 66 60

11. On a coordinate plane, the four corners of Ronald’s garden are located at (0,2), (4, 6), (8, 2) and (4, -2). Which of the following most accurately describes the shape of Ronald’s garden? square rectangle rhombus trapezoid parallelogram

12. Find x and y so that ABCD will be a parallelogram. 24˚ X = 6, y = 42 (y-10)˚ 32˚ X = 6, y = 22 4x B C X = 20, y = 42 X = 20 , y = 2 X = 8, y = 34

13. In trapezoid DEFG, find the measure of angle D. 136 72 D G 28 72 108 136 44

14. For rhombus GHJK, find angle 1. 22⁰ H 68 22 44 90 111

15. Determine whether ABCD is a parallelogram. Justify your answer. Yes; opposite sides congruent (T6.9) D C No; not enough information Yes: opposite sides parallel (def’n of parallelogram) Yes; opposite angles congruent (T6.10) Yes; opposite sides congruent (T6.3)

16. Given rectangle ABCD, find the measure of angle ABD. 9 3x + 6 21 5x - 4 B C 51 39 44

17. Name the missing coordinates for the rectangle with length twice the width. B(0,a) C(2a, b) , D(2a, 0) C(2a,a) , D(2a, 0) A(0,0) D(?,?) C(a, b) , D(a, 0) C(a, b) , D(0, a) C(2a, b) , D(0, 2a)

18.Give the reason for the second line in the proof Given: ABCD is parallelogram Prove: AC ≠ BD B C given statement reason ABCD is parallelogram given AD ≅ CB ? CPCTC substitution T6.3; opposite sides of a parallelogram are congruent T 6.9; opposite sides congruent make a parallelogram