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Honors Geometry
Midterm Review: Chapter 5-7
Name ______________________________________
What is the most descriptive name for each quadrilateral below?
1.
2.
3.
4.
6
10
5.
8
6.
7.
8.
10
Give the MOST DESCRIPTIVE name for each polygon. All of them are NOT quadrilaterals!
9. A four-sided figure in which the diagonals are perpendicular
bisectors of each other.
10. A four-sided figure in which the diagonals bisect each other.
11. A triangle in which there is a hypotenuse.
12. A four-sided figure in which the diagonals are congruent and
all sides are congruent.
13. Each angle of a regular polygon is 168°.
14. The figure formed by joining consecutive midpoints of a
rectangle.
15. The polygon that contains 35 diagonals.
16. A quadrilateral whose consecutive sides measure 15, 18, 15,
and 18.
17. The sum of the measures of the angles of the polygon is equal 18. The sum of the angles of a polygon is 1800°.
to twice the sum of the measures of the exterior angles, one per
vertex.
19. A quadrilateral with consecutive angles of 30°, 150°, 110°,
and 70°.
Find each value specified.
21. Two consecutive angles of a parallelogram are in a ratio of
7:5. Find the measure of the larger angle.
20. Each exterior angle of the polygon is 40°.
22. The measure of one angle of a parallelogram is 40 more than
3 times another. Find the measure of each angle.
FGHJ parallelogram
23. Given: FG = x + 5, GH = 2 x + 3
m∠G = 40°, m∠J = (4 x + 12)°
Find:
a) m∠F
b) Perimeter of FGHJ
Find: m∠B
j // k
25. Given: m∠1 = x 2 − 4 x
m∠2 = 3 x + 18
Find: x and m∠8
ABCD parallelogram
m∠A = (3x + y )°
24. Given:
m∠D = (5 x + 10)°
m∠C = (5 y + 20)°
n // m
26. Given: m∠1 = 157°
m∠3 = 39°
j
k
3 7
8 1
4 5
6 2
Find: the measure of each of the numbered angles
1 2
27. Find the value of x.
n
56 7
28. Given:
m∠ABC = 60°
m∠ACB = 70°
Find: m∠BFC
3 4
m
29. MAST is a rhombus. Find the m∠MAS.
m∠A = 120°
A
30. Given: BE and BD trisect ∠ABC
CD and CE trisect ∠ACB
(x2)°
Find: m∠D and m∠E
(6x+40)° M
S
T
31. EASY is an isosceles trapezoid with bases EY and AS .
Find AS.
E
Y
(x + 60)°
32. The consecutive sides of a quadrilateral measure (x−17),
(24−x), (3x−40), and (x+1). The perimeter is 42. Is the figure a
parallelogram? Explain your answer.
(4x)°
A
33. ABCD is a rectangle.
m∠BAC = 3x + 5
S
x−3
A
m∠ACD = 40 − 2 x
B
E
Find m∠AED
D
34. ABCD is a rhombus. m∠ABC = 110°
Find the measure of each angle in the picture.
A
D
C
B
C
35. The measures of the angles of a triangle are in the ratio 1:2:3. Find half the measure of the largest angle.
m∠PST = (x + 3 y )°
36. Given: m∠P = 45°, m∠R = (2 y )°
m∠PSR = (5 x )°
37. Use the diagram of ∆XYZ where U, V, and W are the
midpoints of the sides.
If UW = 4x − 1 and YZ = 5x + 4, find UW.
Find: m∠PST
Complete the following probability questions.
38. If one of the four angles of parallelogram ABCD is selected at
random, what is the probability that the angle is congruent to ∠C?
39. If two of the five labeled angles are chosen at random, what is
the probability that they are supplementary?
40. Two polygons are selected at random from a group consisting
of a non-isosceles trapezoid, an isosceles trapezoid, and a
parallelogram. Find the probability that both polygons have two
pairs of congruent angles.
41. The angles of a rectangle and a parallelogram that is not a
rectangle are in a box. If two of the eight angles are selected at
random, what is the probability that the angles are congruent?
Complete the following CROOK problems.
42. Find the value of x.
43. Find the m∠1.
50°
x°
70°
44. Find the value of x.
45. Find the value of x.
Determine if the lines are parallel. Explain your reasoning.
46. Are line a and b parallel?
47. Are lines m and p parallel?
Use polygon formulas to help find each specified value.
48. The sum of the angles of an equiangular polygon is 3960°.
Find the measure of each exterior angle.
49. Find the sum of the measures of the angles of a nonagon.
50. Find the value of x.
51. How many diagonals does a heptagon have?
52. Find the measure of each angle of an equiangular
pentadecagon.
53. Find the measure of each exterior angle of a regular
dodecagon.
54. Find the measure of each angle in the picture where ABCDEF
is a regular hexagon.
55. Find the measure of each angle in the picture where RHOAD
is a regular pentagon.
R
H
D
O
A
Determine if each statement is ALWAYS, SOMETIMES, or NEVER true.
56. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, the quadrilateral is a kite.
57. If A, B, C, and D are noncoplanar, AB ⊥ BC , and AB ⊥ BD , then AB is perpendicular to the plane determined by B, C, and D.
58. Two parallel lines determine a plane.
59. Planes that contain two skew lines are parallel.
60. If the diagonals of a quadrilateral are congruent, the quadrilateral is an isosceles trapezoid.
Determine if each statement is ALWAYS, SOMETIMES, or NEVER true.
61. If the diagonals of a quadrilateral divide each angle into two 45-degree angles, the quadrilateral is a square.
62. If a parallelogram is equilateral, it is equiangular.
63. If two of the angles of a trapezoid are congruent, the trapezoid is isosceles.
64. An exterior angle of a triangle is larger in measure than any angle of a triangle.
65. If two pairs of angles are congruent in two triangles, then the third pair of corresponding angles must be congruent also.
Answer ALWAYS, SOMETIME, or NEVER: A
quadrilateral is a parallelogram if
66. Diagonals are congruent.
67. One pair of opposite sides is congruent and one pair of opposite sides is parallel.
68. Each pair of consecutive angles is supplementary.
68 ½ ☺ All angles are right angles.
Determine if each statement is TRUE or FALSE.
69. The diagonals of a rectangle are perpendicular to each other.
70. Two lines must either intersect or be parallel.
71. In a plane, two lines perpendicular to the same line are parallel.
72. In space, two lines perpendicular to the same line are parallel.
73. If a line is perpendicular to a plane, it is perpendicular to every line in the plane.
74. It is possible for two planes to intersect at one point.
75. If a line is perpendicular to a line in a plane, it is perpendicular to the plane.
Determine if each statement is TRUE or FALSE.
76. Two lines perpendicular to the same line are parallel.
77. A triangle is a plane figure.
78. A line that is perpendicular to a horizontal line is vertical.
79. Three parallel lines must be coplanar.
80. Every four-sided figure is a plane figure.
81. Two planes perpendicular to the same line are parallel.
82. Lines that never meet are parallel.
83. If two points of a line lie on a plane, then the entire line lies on the plane.
84. Skew lines are noncoplanar.
85. Two intersecting lines determine a plane.
Complete the following restriction problems.
86. Find the restrictions on x.
87. Find the restrictions on x.