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Honors Geometry
Chapter 6 Review
Name_______________________________
1. Find the measure of each interior angle in an equiangular decagon.
2. Find the sum of the measures of the angles of a pentagon.
3. Find the sum of the measures of the exterior angles of a 30-gon.
4. If the sum of the measures of the angles of a polygon is 3060°, how many sides does the polygon have?
5. Find the measure of each exterior angle of a regular heptagon. Round to the nearest tenth.
6. Does there exist a regular polygon in which each exterior angle has a measure of 37°30′?
7. The measure of each exterior angle of an equiangular polygon is 13
1
. How many sides does the polygon have?
3
8. The length of one base of a trapezoid is 19 inches and the length of the midsegment is 16 inches. Find the length of the other base.
For numbers 9 & 10, give the most descriptive name for each polygon.
9. Each interior angle is 144°.
10. The measure of each interior angle is 3 times the measure of each exterior angle.
11. Determine whether the quadrilateral ABCD with vertices A(0, 1), B(4, 3), C(5, −1), D(−1, −7) is a kite. Justify your answer.
X
12. HEXAON is a regular hexagon. Find the value x.
A
E
For numbers 13 – 15, use the figure to the right.
x° G
O
H
N
P
1
13. If 1  2, what two lines must be parallel?
A
O
14. If PARD is a parallelogram, then PO must be congruent to what other segment?
2
D
15. If PARD is a rhombus, then what kind of angle is mPOD?
For numbers 16 – 18, give the most descriptive name for each quadrilateral.
5
16.
7
R
17. A quadrilateral with each pair of consecutive angles supplementary.
18. A quadrilateral whose congruent diagonals are perpendicular bisectors of each other.
For numbers 19 – 22, choose the correct answer.
19. Each of the following quadrilaterals always has congruent diagonals except
a) a rectangle
c) an isosceles trapezoid
e) all of them always have congruent diagonals
b) a kite
d) a square
20. Which of the following is not a property of parallelograms?
a) Both pairs of opposite sides are congruent.
c) The sum of the angles is 360°.
e) Diagonals are perpendicular.
b) Diagonals intersect at their midpoints.
d) Consecutive angles are supplementary.
21. Which statement is not always true?
a) The diagonals of a parallelogram bisect the angles of the parallelogram.
b) The diagonals of a rhombus are perpendicular bisectors of each other.
c) The diagonals of an isosceles trapezoid are congruent.
d) One diagonal of a kite bisects the other diagonal.
e) The diagonals of a rectangle are congruent.
22. Which pairs are equilateral quadrilaterals?
a) parallelogram and rectangle
b) trapezoid and rhombus
c) square and rhombus
d) square and rectangle
e) isosceles trapezoid and square
23. Given rectangle MATH, MG = x + y + 1, AG = 2x + 3y, TG = 3x + 6y + 6. Find TM.
M
A
G
For numbers 24 – 34, write A for always, S for sometimes, or N for never.
H
24. If a parallelogram has congruent diagonals, then it is a square.
25. The diagonals of a rhombus are congruent.
26. If one of the angles of a parallelogram is a right angle, then all of the other three angles must be right angles.
27. The diagonals of a parallelogram are congruent.
28. In a quadrilateral, if one diagonal bisects opposite angles, then it is a kite.
29. A rhombus is a trapezoid.
30. If ABCD is an isosceles trapezoid, then A is supplementary to C.
T
31. The diagonals of an isosceles trapezoid bisect each other.
32. If the diagonals of a quadrilateral bisect each other, then it is a trapezoid.
33. A diagonal of a parallelogram divides it into two congruent triangles.
34. If both pairs of opposite angles in a quadrilateral are congruent, then it is a rhombus.
For numbers 35 – 39, answer true or false. Answer true only if the statement is always true.
35. A square is a rectangle.
36. An isosceles trapezoid has two congruent diagonals that bisect each other.
37. A trapezoid has a pair of opposite sides parallel.
38. A rectangle is a rhombus.
39. In a kite two pairs of opposite angles are congruent.
For numbers 40 & 41, decide whether the four points form a parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid,
or kite. Use the most specific name possible.
40. A(–2, 3), B(–2, –4), C(2, –4), D(2, 3)
-10 -8
-6
-4
10
10
8
8
6
6
4
4
2
2
-2
2
4
6
8
10
-10 -8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
42. Given: ABCD is a parallelogram
Find: mD.
D
D
41. M(1, 1), N(–2, 4), P(–5, 1), Q(–2, –2)
K
J
M
F
A
A
(3x + 2)°
B
6
8
10
43. FHJK is a rhombus, KM = 6 and MJ = 8
Find the perimeter of the rhombus.
C
(x + 62)°
4
H
44. Given that PQRS is a kite, find x.
45. Find the length of EF in parallelogram EFGH.
S
4x
P
(7x + 4) º
T
2x – 5
E
D
(x + 21)°
F
R
(3x + 1)º
G
Q
46. Given: BRAY is an isosceles trapezoid.
BA = 13
YN = 2x – 1
NR = x + 5
Find NR.
Y
(4x)°
H
A
N
B
R
For numbers 48 – 53, give the most descriptive name for each of the following:
47.
48.
49.
50.
51.
52.
53. ABCD is a rhombus, mDAB = 120°, AE = 5. Find the perimeter of the rhombus.
A
B
E
C
D
54. ABCD is a rhombus, mDAB = 120°, the perimeter is 64. Find EC.
A
B
E
D
C