CP Geometry Midterm Review Packet
Total Page：16
File Type：pdf, Size：1020Kb
CP Geometry Midterm Review Packet Name:______Date:______
True or False:
1.______Every line segment has one and only one midpoint.
2. ______If two angles are equal, they are right angles.
3. ______If two angles are supplementary, then they are equal.
4. ______Two points determine one and only one plane.
5. ______An angle has one and only one bisector.
6. ______The sum of two acute angles is an obtuse angle.
7. ______If a triangle is equilateral, then it is isosceles.
8. ______Since the sum of 20°, 30°and 40° is 90°, then the angles are complementary.
9. ______Every polygon has more than three sides.
10. ______The sum of the interior and exterior angles of a pentagon are the same.
Set up and solve the following word problems.
11. Two angles are supplementary. Find the angles if one angle is 45°more than twice the other angle.
12. Two angles are complimentary. If one angle is 32° less than the other, Find the angles. 13. Two angles are supplementary. Find the angles if one angle is 10°more than two- thirds the other angle.
14. In a triangle,
15. ΔABC is isosceles and one of the base angles is 15° larger than the vertex angle. Find the angles.
16. In a triangle,
17. Find the sum of the interior angles of a heptagon.
18. Find the number of degrees in each exterior angle of a regular octagon.
19. How many sides does a polygon have if the sum of its interior angles is 1800°?
20. How many sides does a regular polygon have if each interior angle is 144°? Solve the following angle problems:
21. A < BED = 52°
B < CED = 28° < AEB = 18° Find < AEC______
C
E D
22. EB bisects < AED A < AED = 74° B < BEC = 19° Find < CED______
C
E D
23. < AEB = 29° 14’ A < CED = 31° 26’ B < BEC = 24° 34’ Find < AED______
C
E D 24. A BC bisects < ABD < ABD = 71° 38’ C Find < CBD______
B D
25. (BE Bisects < ABC) < ABD = 56° < DBC = 28° Find < ABE______
A < E
D
B C
26. A < ABE = 83° 14’ C < ABC = 23° 48’ < CBD = 27° 17’ Find < DBE = ______D
B E 27. ∆ABC is isosceles with base AC. m< A = 3xm< B = 4x Find x = ______m< A= ______m< B = _____ m< C=_____ B
A C
28. ΔABC is isosceles with base AC. m< BCD = 110° Find m< A ______m< B ______m< ACB______B
A C D
Draw the segment and then solve.
29. B is the midpoint of AC . AC = _____ AB = _____ AC = x + 3 BC = _____ AB = x
AC = _____ AB = _____ BC = _____ 30. B is between points A and C. AB = 4x – 1 BC = 2x + 3 AC = 8x 31. Find the sum of the measures of the interior angles of a 11-gon.
______
32. The measure of each exterior angle of a polygon is 45o. Find the number of sides of the polygon.
______
33. Find the measures of an interior and exterior angle of a regular pentadecagon.
______
34. The measure of an interior angle of a regular polygon is 120o. Find the number of sides of the polygon.
______
35. If the exterior angle of a regular polygon measures 36o, find the sum of the measures of the interior angles.
______36. 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.
______37. The sum of the interior angles of a polygon are 900o. Name the polygon.
______
38. 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.
39. Δ DOG ≈ Δ ______BY:______
C D
A O G T
40. Δ BID ≈ Δ______BY:______I
B D R
41. Δ SAN ≈ Δ______BY:______
S N
A
E K
42. Δ GTA ≈ Δ______BY:______
G
O
T
A 43. Δ ABD ≈ Δ______BY:______Given < ADB ≈ < CDB A
B D
C
44. Δ ABC ≈ Δ______BY:______D
A C
E
B
Use the following sketch to solve: C
A B D
E F H
G
45. < ABF = 6x – 16 < BFH = 2x +28 Find X ______< EFB______< CBD______46. < DBF = 5x + 16 < BFH = 3x + 12 Find X______< ABF______< EFB______
Solve: 47. 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.
48. 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.
49. 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.
Use the following sketch for # 50 – 55. A E G
7 5 8 F 6
3 B 1 4 2 C D H
50. List all Alternate Interior angles.______
51. List all Alternate Exterior angles.______
52. List all Corresponding angles.______
53. List all Same side interior angles.______
54. If < ABC = 108° then < GFH =______; < HFB=______
55. If < DBF = 95°, then < BFH=______; < BFE=______A B I 56.
C D E
F G H
ABP CE P FH �ABD 32 �BDG 89 �EDG ______�DGH ______
E
57. A F B 5x+16 ABP CD �BFG ______C G 3x+12 D �FGD ______
H
E
A F B 58. AB || CD 6x - 16 A E H B G F C D 59. BF || CD EC bisects Simplify each radical expression 17 60. 4 600 61. 62. 4 96 2 54 3 Set up the following ratio and reduce to lowest terms. 63. 10 inches to 3 feet ______ 64. 30 minutes to 5 hours ______ 65. 5 3 to 27 ______ Solve the proportion. 7 9 4 3 2 66. 67. x 27 3 x 16 x 7 5 x 68. 69. x 4 2 5 8 5 Are the triangles similar? If so, write a similarity statement and identify the postulate or theorem that justifies your answer. 70. A D G 92° 68° 23° C T 92° O 10 71. S L N 8 15 20 6 M A B 25 72. B Z 24 Y 32° 12 44 A 9 C 32° X Use the given information to determine the similar triangles. Then, solve for the missing side. 73. Given AG YM. Y RA = 5 A AG = 6 YM = 15 Find RM = ____ R G M 74. Given AB DE. A B AB = 2 5 AC = 4 3 C ED = 5 6 Find CD = ______ D E 75. Find x and y in the diagram below if EB DC. D DC = 27 AD = 33 E AB = 20 AC = 30 x Find x = _____ y Find y = _____ A B C 76. If ABC ~ QPR , m < A = 30° and m < B = 97°, find the measures of angles Q, P, and R. m < Q = _____ m < P = ______m < R = ______ 77.-79 Use the diagram at the right to the answer the next 3 questions. 77. If AB=3x+8 and GJ=2x+24, what is AB? ______ 78. If AC=3y-5 and HJ=4y+2, what is HB? ______ 79. If GH=7z-1 and BC=4z-3, what is GH? ______80-83. Is this triangle possible? 9. 2.5, 3.5, 5 ______10. 2, 6, 9 ______11. 9, 12, 15 ______ 84-85. Find the third side. Write an inequality statement. 84. 5, 15, ______85. 8, 22, ______ 86-87 Find the missing angles. 86. 87. 88-91 Use the diagram to the right. 88. If AB=BC, and m B=75, then the longest side is ______. 89. If m A=90, then the longest side is ______. 90. If AB=8, BC=6 and AC=13, then the largest angle is ______. 91. If AB=5, BC=7, and AC=10, then the smallest angle is ______.