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Geometry
Trimester 1 Final Review
Name______________
Show all work!!! This review is worth points on your final exam. It must be turned in when you come to
the exam. Under NO CIRCUMSTANCES will it be accepted late and you will not be allowed to go to your
locker to get it.
1. Explain the difference between GH and GH . Draw pictures to go along with this explanation.
2. Explain the difference between JK and JK .
3. Explain whether MN and NM mean the same thing. What about ST and TS ? Pictures should
accompany explanations.
4. Explain what it means for two rays to be opposite rays. Draw a picture to go along with
this explanation.
5. Explain what it means to bisect something.
6. Explain what a counterexample is.
7. Explain what it means for two lines to be perpendicular to each other. What is the symbol for
perpendicular?
8. If you have two parallel lines cut by a transversal, name 4 things you know:
1.
2.
3.
4.
9. What are the 5 ways to prove triangles congruent?
1.
2.
3.
4.
5.
10. What does CPCTC stand for? When can/should you use it?
11. What does it mean for a triangle to be isosceles? Draw an example.
12. What does it mean for a triangle to be equilateral? Draw an example. If the triangle is equilateral
what else do we know about it?
For problems 19-30, draw a picture (and label it) to go along with the given information.
13. M is the midpoint of GH .
14. TW bisects STU .
15. AED And CEB are acute, vertical angles.
16. XYSand SYZ form a linear pair.
17. QRT and TRS are complementary,
18. QRST is equiangular but not equilateral.
adjacent angles..
19. ABCDE is a concave pentagon.
20. ΔABC  ΔDEC by SAS
21. j // k. 1 and 2 are alternate interior angles.
22. ΔJKL  ΔMKL by HL
23. NH  ST
24. M is the midpoint of LN . Find LN.
25. M is the midpoint of AC . Find AM.
26. BD bisects ABC . Find mABC .
27. BD bisects ABC . Find mABC .
For problems 28-30, find the coordinates of the midpoint of AB and then find AB.
28.
A(0, 2)
29.
A(1, 4)
30.
A(-4, -2)
B(-3, 8)
B(5, 1)
B(3, -7)
For problems 31 – 33, use the information to find the indicated measure.
31.
Area = 504 in2
32.
Circumference = 40π in
Find the height h.
Find the area.
33. Perimeter = 60 cm
Find the length of
each side.
5x+1
r
3x-3
34. Identify all of the pairs of corresponding
angles in the diagram.
35. Identify all of the pairs of alternate
interior angles in the diagram.
36. Identify all of the pairs of alternate
exterior angles in the diagram.
37. Name 4 pairs of vertical angles.
38. Identify all of the pairs of same-side
interior angles in the diagram.
39. Name 4 linear pairs.
Find all the unknown angle measures in the diagram.
40. 1
41. 2
42. 3
43. 4
44. 5
45. 6
Decide if each argument is valid or invalid. If it is valid, tell what rule of logic it uses. If it is
invalid, give a counterexample.
46. If today is Monday, then I go to school. Today is not Monday. Therefore, I do not go to school.
47. Jim or Mark dropped the pass. Mark did not drop the pass. Therefore, Jim dropped the pass.
48. If Amy hits a home run, then she is credited with an RBI. Amy is not credited with an RBI.
Therefore, Amy did not hit a home run.
49. If you are at Osseo Senior High, then you are in Minnesota. If you are in Minnesota, then you are in
the United States. Therefore, if you are in the United States, you are at Osseo Senior High.
For the statement, rewrite it in if-then form. Then write the converse for the statement. Decide if
each statement is true or false. If false, provide a counterexample.
50. A six-sided polygon is a regular hexagon.
If – then: ______________________________________________________
True or False
Converse: _______________________________________________________
True or False
51. A right angle is 90°.
If – then: ______________________________________________________
True or False
Converse: _______________________________________________________
True or False
Find x.
52.
53.
54. In the diagram, RS  ST .
Find the value of x and y.
55.
56.
Proofs
57.
Given:
Prove:
Statements
58.
Given: p //t; q // r
Prove: 1  3
Statements
59.
Reasons
Reasons
Given: j // k
Prove: 1 is supplementary to 5
Statements
Reasons
j
q
1
4
5
k
60.
Given: p // r; 1  2
Prove: h // g
Statements
g
h
Reasons
p
3
1
r
2
MN  PQ, MQ  NP
Prove: ΔMNQ  ΔPQN
61. Given:
Statements
62.
Reasons
B
Given: AD  BE
Prove:
AD bisects BE
AB  DE
B  E
Statements
Reasons
C
A
E
63.
Given: T  V
SU  TV
Prove: ΔSTU  ΔSVU
Statements
Reasons
D
64.
Given: B is the midpoint of AE .
B is the midpoint of CD .
Prove: D  C
Statements
65.
Reasons
Given: JT  JR
JM  TR
Prove: ΔTMJ  ΔRMJ
Statements
Reasons