Download CP GEO Midterm RP ANSWERS

CP Geometry Midterm Review Packet
Name:_________________
Date:_______________
True or False:
1._True _ Every line segment has one and only one midpoint.
2. _False_ If two angles are equal, they are right angles.
3. _False_ If two angles are supplementary, then they are equal.
4. _False__ Two points determine one and only one plane.
5. _True__ An angle has one and only one bisector.
6. _False__ The sum of two acute angles is an obtuse angle.
7. _False__ Every rectangle is a square.
8. _True_ If the diagonals of a quadrilateral are equal, then the figure is a
rectangle.
9. _False_ A trapezoid is a parallelogram.
10. _True__ A square is a rhombus.
11. _True_ If a triangle is equilateral, then it is isosceles.
12. _False_
Since the sum of 20°, 30°and 40° is 90°, then the angles are
complementary.
13. _True_ A rectangle may be equilateral.
14. _False_ Every polygon has more than three sides.
15. _False_ The sum of the interior and exterior angles of a pentagon are
the same.
Set up and solve the following word problems.
16. Two angles are supplementary. Find the angles if one angle is 45°more
than twice the other angle.
M< 1 = x
M<2 = 2x + 45
x  2 x  45  180
3 x  45  180
3 x  135
X = 45 o and 135
o
x  45
17. Two angles are complimentary. If one angle is 32° less than the other,
Find the angles.
m<1 = x
m<2 = x – 32
x  x  32  90
2 x  122
X = 61 o and X = 29
o
x  61
18. Two angles are supplementary. Find the angles if one angle is 10°more
than two- thirds the other angle.
2
x  x  10  180
3
m<1 = x
X = 102° and X = 78°
3
2
2
x  x  170
m<2 = x  10
3
3
3
5
x  170
3
x  102
19. In a triangle, <B is 12° larger than <A. <C is equal to the sum of the first
two angles. Find the angles.
m<A = x
m<B = x + 12
m<C = 2x + 12
4 x  24  180
4 x  156
x  39
m<A =39°
m<B = 51°
m<C = 90°
20. ΔABC is isosceles and one of the base angles is 15° larger than the
vertex angle. Find the angles.
m< A = x
m< B = x + 15
m<C = x + 15
3x  30  180
3x  150
x  50
m<A = 50°
m<B = 65°
m<C = 65°
21. In a triangle, <B is 2 times as large as <A. If <C is 4° less than <A, find all
three angles.
4 x  4  180
m<A = x
m<A = 46°
4 x  184
m<B= 2x
m<B = 92°
m< C = x – 4
m<C = 42°
x  46
22. Find the sum of the interior angles of a heptagon.
7 – 2(180) = 5(180) = 900°
23. Find the number of degrees in each exterior angle of a regular octagon.
360  8 = 45°
24. How many sides does a polygon have if the sum of its interior angles is
1800°?
1800 = (n-2)180
12 sides or a dodecagon
10 = n – 2
12 = n
25. How many sides does a regular polygon have if each interior angle is
144°?
Exterior Angle = 180 -144 = 36
360  36 = 10 sides or a decagon.
Multiple Choice:
26. By definition, a parallelogram is a quadrilateral whose:
a. opposite sides are equal
b. opposite sides are parallel
c. diagonals bisect each other d. all of the above
27. The opposite angles of a parallelogram are:
a. equal
b. supplementary c. complimentary
28. Every trapezoid is a :
a. square
b. quadrilateral
c. parallelogram
29. In general, if the diagonals of a quadrilateral bisect each other, the
quadrilateral is a :
a. Square
b. Rhombus c. Parallelogram d. rectangle
30. In general, if the diagonals of a quadrilateral are equal, the
quadrilateral is a:
a. Rectangle
b. Rhombus
c. trapezoid
31. If the diagonals of a quadrilateral bisect each other at right angles, the
figure is a :
a. Rectangle
b. Trapezoid
c. Rhombus
State always, sometimes, or never:
32. A square is a rhombus.
Always
33. A rhombus is a square.
sometimes
34. A trapezoid is a parallelogram.
never
35. A trapezoid may be equilateral.
never
36. A rectangle is a square.
sometimes
Solve the following angle problems:
37.
< BED = 52°
< CED = 28°
< AEB = 18°
Find < AEC =___42°________
A
B
C
E
D
38.
EB bisects < AED
< AED = 74°
< BEC = 19°
Find < CED___18°________
A
B
C
D
E
39.
< AEB = 29° 14’
< CED = 31° 26’
< BEC = 24° 34’
Find < AED__85° 14’____
A
B
C
D
E
A
40.
BC bisects < ACD
< ABD = 71° 38’
Find < CBD_35°49’______
C
B
D
41.
(BE Bisects < ABD)
< ABD = 56°
< DBC = 28°
Find < ABE____42°____
A
E
D
B
42.
C
< ABE = 83° 14’
< ABC = 23° 48’
< CBD = 27° 17’
Find < DBE = __32° 09’___
A
C
D
E
B
43. ∆ABC is isosceles with base AC. BD is the perpendicular bisector of AC.
AB = 5 and AC = 8 < ABD = 40°
Find BC= ____5___
m< C = __50°____
B
A
D
C
m< BDA =___90°_____
44. ∆ABC is isosceles with base AC.
m< A = 3x
m< B = 4x
Find x = __18__ m< A= ___54°__
m< B = _72°_
B
m< C=_54°__
3x + 3x + 4x = 180
10x = 180
X = 18
A
C
45. ΔABC is isosceles with base AC.
m< BCD = 110°
Find m< A __70°___
m< B __40°___
m< ACB___70°___
B
40°
70°
A
70°
110°
C
Draw the segment and then solve.
45. B is the midpoint of AC .
AC = x + 3
A
AB = x
D
B
C
AC = _6__
AB = _3___
BC = _3___
46.
B is between points A and C.
AB = 4x – 1
BC = 2x + 3
AC = 6x
AC = _____
AB = _____
BC = _____
Solve:
47. If one angle in a parallelogram contains 39º, find the numbers of
degrees in the other three angles.
m< 1 = 39 º
m< 2 = 39 º
m< 3 = 141 º
m< 4 = 141 º
48. Two opposite angles in a parallelogram are 5x – 4 and 80 – x. Find the
number of degrees in all four angles.
5x – 4 = 80 – x
6x = 84
X = 14
m< 1 = m< 2 = 66 º
m< 3= m< 4 = 114 º
49. If two opposite sides of a parallelogram are 3x + 2 and 5x – 8 and the
sum of any two consecutive sides is 37, find the length of each side of the
parallelogram.
3x + 2 = 5x – 8
side 1 = side 2 = 17
10 = 2x
side 3 = side 4 = 20
X=5
50. Find x and AC.
B
C
D
A
BD = 3x + 20
AC = 6x – 16
3x + 20 = 6x - 16
3x = 36
X = 12
51. . Given parallelogram ABCD.
BE = 3x + 8
BD = 5x + 20
B
C
E
A
D
x = _12_____
AC = _56___
x = __4___
ED = __20___
2(3x + 8) = 5x + 20
6x + 16 = 5x + 20
X=4
52. Given parallelogram ABCD.
A  5 x  22
B  3x  6
x = ___19____
D. = __63 º ___
B
C
E
A
D
53. BAE  25x  30
B
5x + 22 + 3x + 6 = 180
8x + 28 = 180
8x = 152
X = 19
Find X = _____3____________
C
25x – 30 = 45
25x = 75
X=3
E
A
D
54. Find x and y for the trapezoid.
x = __11__
10x + 5
5x + 10
4y - 1
y = __16.5 º__
10x+5+5x+10 = 180
15x + 15 = 180
15x = 165
X = 11
65 = 4y - 1
66 = 4y
y = 16.5
55. Find the sum of the measures of the interior angles of a 11-gon.
( 11 – 2) 180
___1620 º ______
56. The measure of each exterior angle of a polygon is 45o. Find the
number of sides of the polygon.
360  45 = 8
_____n = 8______
57. Find the measures of an interior and exterior angle of a regular
pentadecagon.
(15 – 2) 180 = 2340  15 = 360
360  15 =
Int =___156 º _ Ext = _24 º_____
58. The measure of an interior angle of a regular polygon is 120o. Find
the number of sides of the polygon.
Int = 120, Ext = 60 º
360  60 = 6 sides
_____n = 6____
59. If the exterior angle of a regular polygon measures 36o, find the sum
of the measures of the interior angles.
360  36 = 10 sides
(10-2)180 = 1440
______1440____
60. If the measure of each of the interior angles of a regular polygon is
100 more than the measure of each of the exterior angles, name the
polygon.
(n  2)180 360

 100
n
n
____nonagon______
 (n  2)180 360

n

 100 
n
n


(n  2)180  360  100 n
180n  360  360  100n
80n  720
n9
61. The sum of the interior angles of a polygon are 900o. Name the
polygon.
(n-2)180 = 900
(n-2) = 5
N=7
___heptagon____
62. The measures of the interior angles of a pentagon are x, 3x, 2x – 1,
6x – 5, and 4x + 2. Find the measure of each angle.
16x + -4 = 540
16x = 544
X = 34
34,67,102,138, 199____
62. Two opposite angles in a parallelogram contain ( 5x – 4)° and ( 80 – x)°.
Find the number of degrees in all 4 angles.
5x – 4 = 80 – x
6x = 84
X = 14
66,66,114,114
64. Δ DOG ≈ Δ _CAT_____ BY:____ASA____________
C
D
A
O
G
T
65. Δ BID ≈ Δ__RID___
BY:_ _SSS_______
I
B
D
R
66. Δ SAN ≈ Δ___KAE_____
S
BY:______SAS________
N
A
E
K
67. Δ GTA ≈ Δ___AOG____
BY:_____HL ________
G
O
T
A
68. Δ ABD ≈ Δ____CBD_____
Given < ADB ≈ < CDB
BY:______SAS__________
A
D
C
B
69. Δ ABC ≈ Δ_EDC_____
BY:____ASA_________
D
A
C
E
B
Use the following sketch to solve:
C
A
B
E
F
D
H
G
70. < ABF = 6x – 16
< BFH = 2x +28
Find X _____11_______
< EFB____130 º ______
< CBD____50_ º ___
71. < DBF = 5x + 16
< BFH = 3x + 12
Find X___19_____
< ABF____69 º_____
< EFB_____111 º_____
Solve:
6x – 16 = 2x + 28
4x = 44
x = 11
5x + 16 + 3x + 12 = 180
8x + 28 = 180
8x = 152
x = 19
72. If two lines are parallel and are cut by a transversal, two alternate
interior angles represented by 3x and 5x – 70. Find the angle measures.
3x = 5x – 70
-2x = -70
X = 35
m<1 = m<2 = 105 º
73. If two lines are parallel and are cut by a transversal, two corresponding
Angles represented by 2x + 10 and 4x -50. Find the angle measures.
2x + 10 = 4x – 50
60 = 2x
30 = x
m<1 = m<2 = 70 º
74. If two lines are parallel and are cut by a transversal, two same side
interior angles represented by 2x and 3x. Find the angle measures.
2x + 3x = 180
5x = 180
X = 36
m< 1 = 72 º
m< 2 = 109 º
Use the following sketch for # 75 – 80.
A
E
G
7
5
8
F
6
3
1
B
4
2
C
H
D
75. List all Alternate Interior angles._____<3 & < 6, _<4 & < 5__________
76. List all Alternate Exterior angles._____<7 & < 2 , <1 & < 8 ________
77. List all Corresponding angles.___<1&<5, <3&<7, <2&<6, <4<8______
78. List all Same side interior angles._____<4&<6, <3&<5_________
79. If < ABC = 108° then < GFH =_108°___; < HFB=_____72°________
80. If < DBF = 95°, then < BFH=__85°____; < BFE=____95°________
81.
A
B
AB CE FH
I
ABD  32
BDG  89
E
D
C
EDG  57
DGH  123
82.
G
F
E
H
AB CD
BFG  __111 __
A
F
5x+16
B
FGD  __ 69 ___
5 x  16  3 x  12  180
8 x  28  180
8 x  152
x  19
E
83. AB || CD
A
F
<AFG = ___50°____
<FGD = ___50°____
B
6x - 16
G
C
2x +28
D
6x – 16 = 2x + 28
4x = 44
X = 11
H
84. BF || CD
EC bisects <ACD
<EGF = 42°
< CBF = ___96°_____
< ABG = __84°____
A
E
42
G
B
F
96
42
42
C
D