Download REVIEW ch 6

Geometry
REVIEW: Chapter 6
Name _____________________________________
1. What is the sum of the interior angles of a polygon with 17 sides?
2. The measure of each interior angle of a regular polygon is 165. How many sides does the polygon have?
3. Find the length of EF in parallelogram EFGH.
E
G
(4x)°
2x – 5
F
(x + 21)°
H
4. Which of the following is a property of a parallelogram?
a) Each pair of opposite sides is congruent.
b) Only one pair of opposite angles is congruent.
c) Each pair of opposite angles is supplementary.
d) There are four right angles.
5. For parallelogram ABCD, find m∠ 1.
6. Given: ABCD is a parallelogram with AE = 9x – 5, AC = 14x + 34. Find AC
A
D
E
B
7. Parallelogram ABCD has vertices A(8, 2), B(6, –4), and C(–5, –4). Find the coordinates of D.
a) D(–5, 2)
b) D(–3, 2)
c) D(–2, 2)
d) D(–4, 8)
8. Which of the following is true for all rectangles?
a) The diagonals are perpendicular.
b) The diagonals bisect the angles.
c) The consecutive sides are congruent.
d) The consecutive sides are perpendicular.
C
9. ABCD is a rectangle. If AC = 5x + 2 and BD = x + 22, find the value of x.
10. Given: ABCD is a rhombus with m1 = (2x)˚ Find: the value of x.
A
B
1
D
C
11. For rhombus GHJK, find m∠ 1.
12. The diagonals of square ABCD intersect at E. If AE = 3x – 4 and BD = 10x – 48, find AC.
13. BRAY is an isosceles trapezoid. BA = 13, YN = 2x – 1, NR = x + 5. Find the value of x.
Y
A
N
B
R
14. Given trapezoid ABCD with median ̅̅̅̅
𝐸𝐹 , which of the following is true?
1
a) EF = AD
b) AB = EF
2
c) AE = FD
d) EF =
𝐵𝐶 + 𝐴𝐷
15. NPQR is a trapezoid. Find the value of x.
2
x+5
N
P
24
R
16. Given that PQRS is a kite, find the value of x.
S
7x + 4
4x
P
T
R
3x + 1
Q
2x – 5
Q
17. JKLM is a kite, find JM.
18. For kite WXYZ, find mW
For numbers 19 – 24, give the most descriptive name for each of the following figures. Choose from isosceles trapezoid, kite,
parallelogram, rectangle, rhombus, and square. Each name will only be used once.
19.
20.
21.
22.
23.
24.
25. What type of parallelogram is figure ABCD with A(–3, 0), B(–1, 4), C(3, 2), and D(1, –2)? SHOW ALL WORK and explain (using
properties) what shape it is and what shape it isn’t.
For 26 – 30, determine if the statement is True or False. Only answer true if the statement is always true.
26. A trapezoid is always a kite.
27. The diagonals of a square are always congruent.
28. A quadrilateral is always a rectangle.
29. A rhombus is always a parallelogram.
30. The diagonals of a parallelogram always bisect opposite angles.