1. Geometry Chapter 6 Review

2. Use paper and pencil to solve. Click on the screen to show the answer.

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

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

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

6. 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

7. 5. Find x for parallelogram ABCD if BC = 3x + 20 and AD = 5x – 12.16 4
10.25
21.5 5

8. 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)

9. 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

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

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

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

13. 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

14. 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

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

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

17. 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)

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

19. 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)

20. 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