Geometry Part 1 Unit 2 Test Review Name__________________Date___________

Geometry Part 1 Unit 2 Test Review Name__________________Date___________

Geometry Part 1 Unit 2 Test Review
Name__________________Date___________
1-12: If mAIB = 53 and mDIE = 46, fill in all angles on the picture and then fill in each blank.
1. mBIC = ______
4. mGIH = ______
2. mFIG = ______
5. mEIF = ______
3. mCID = ______
6. mHIA = ______
7. BID and __________ are a linear pair.
C
B
D
E
A
I
H
8. HIG and __________ are vertical angles.
F
G
9. AIB and __________ are complimentary angles.
10. mDIE + mEIF = m__________. This is an example of the ________________________________
11. AID and __________ are supplementary angles.
12. Is ray IH the bisector of AIG?__________ How do you know?________________________________
13-18: Write the conclusion of each statement using the law of detachment or the law of syllogism.
13.
If Tom does his homework, he will understand proofs.
Tom did his homework last night!
Conclusion:_________________________________________ Law: ________________________
14.
If John goes camping, then Lou will go.
If Lou goes, then Cindy will go.
John went camping!
Conclusion:_________________________________________ Law: ________________________
15.
If two angles are vertical, then they are congruent.
1  2
Conclusion:_________________________________________ Law: ________________________
16.
If a number is a whole number, then it is an integer.
If a number is an integer, then it is a rational number.
Conclusion:_________________________________________ Law: ________________________
17.
If 2 angles are complementary, then the sum of their measures is 90.
A and B are complementary.
Conclusion:_________________________________________ Law: ________________________
18.
If an animal is a fish, then it can swim.
Rufus can swim.
Conclusion:_________________________________________ Law:_________________________
19-21: Is the following conditional statement true? If true, write its converse. If the converse is true, then
write the statement in biconditional form.
19.
If the sum of the measures of 2 angles equals 180, then they are supplementary.
20.
Converse:
21.
Biconditional: ______________________________________________________.
______________________________________________________.
T
F
T
F
22-27: Use the given statement to answer each. Given: My teacher will be happy if I ace this test!
22. Rewrite it in if-then form.____________________________________________________________
23. State the hypothesis._______________________________________________________________
24. State the conclusion.________________________________________________________________
25. State the converse._________________________________________________________________
26. State the inverse.__________________________________________________________________
27. State the contrapositive._____________________________________________________________
28-31: Write the symbolic statement in words given p: C is an acute angle and q: mC is 30.
28. q  p
________________________________________________________________________
29. ~q  ~p
________________________________________________________________________
30. ~p
________________________________________________________________________
31. ~p  ~q
________________________________________________________________________
32-52: Justify each statement with a definition, property, postulate, or theorem.
*(Draw a picture)
32. P  P
_____________________________________
33. If RS = TW, then TW = RS.
_____________________________________
34. If 5y = -20, then y = -4.
_____________________________________
35. 2(a + b) = 2a + 2b
_____________________________________
36. If 2x + y = 70, and y = 3x, then 2x + 3x = 70.
_____________________________________
37. If AB  CD and CD  EF , then AB  EF .
_____________________________________
38. If 2z – 5 = -3, then 2z = 2.
_____________________________________
39. If m1 + m2 = 180, then 1 and 2 are supplementary.
_____________________________________
40. If m1 = 90, then 1 is a right angle.
_____________________________________
41. If m1 = m2, then 1  2.
_____________________________________
42. If AB = CD and RS = TU, then AB + RS = CD + TU.
_____________________________________
43. If 1 and 2 are complementary, then m1 + m2 = 90.
_____________________________________
44. *If ER bisects DEF, then DER  REF
_____________________________________
45. *If B is between A and C, then AB + BC = AC.
_____________________________________
46.
If
1
2
,then 1  2.
_____________________________________
47. If 3and 4 are right angles, then 3  4.
48. If a  b, then 7 is a right angle.
49. If C D and D  E, then C  E.
_____________________________________
a
7
8
_____________________________________
b
_____________________________________
50. If C  E, then mC = mE.
_____________________________________
51. If AB = CD and AB = EF, then CD = EF.
_____________________________________
52. If
1
2
, then 1 and 2 are supplementary.
_____________________________________
53-55: Construct a Venn diagram illustrating the following two statements:
53. Some triangles have acute angles.
54. All right angles are congruent.
55. No child likes spinach.
56-58: Two hundred people were asked what kind of literature they liked to read. They could choose among
novels, poetry, and plays. Answer the questions based on the results in the Venn diagram shown.
Novels
45
56. How many people said they like all three types of literature?
5
57. How many people like to read poetry?
Poetry
6
58. How many people like novels and plays, but not poetry?
59-66: State True or False. If false, give a counterexample to the right of your blank below.
59. Three collinear points are contained in only one plane.
______________
60. If 2 lines intersect, their intersection is a plane.
______________
61. A line may lie in more than one plane.
______________
62. If 2 angles are complementary, then they are adjacent.
______________
63. 3 non-collinear points are contained in more than one plane. ______________
64. The intersection of 2 planes is an infinite number of points.
______________
65. 3 points are always collinear.
______________
66. 2 points are always collinear.
______________
67: Complete the algebraic proof with the correct statement or reason.
Given:
Prove:
8x – 10 = 2(x + 4)
x=3
Statements
Reasons
a. 8x – 10 = 2(x + 4)
a. _______________________________
b. _____________________
b. Distributive Property of Equality
c. 6x - 10 = 8
c. _______________________________
d. 6x = 18
d. _______________________________
e.
e. _______________________________
x=3
38
72
8
Plays
26
68-69: Write an equation and solve for x in each problem.
4x + 11
68.
3x + 1
69.
4x - 26
3x + 4
70: Know the following definitions, postulates, and statements and how to do problems with them:



















Angle Addition Postulate
Angle Bisector
Between
Biconditional
Complementary angles
Compound Statement
Conclusion
Conditional Statement
Congruent
Conjecture
Conjunction
Contrapositive
Converse
Counterexample
Deductive Reasoning
Disjunction
Hypothesis
Inductive Reasoning
Invalid



















Inverse
Law of Detachment
Law of Syllogism
Linear Pair
Midpoint
Negation
Perpendicular Lines
Postulate
Proof
Reflexive
Right Angle
Segment Addition Postulate
Symmetric
Supplementary angles
Theorem
Transitive
Truth Value
Venn Diagram
Vertical Angles