Geometry
Chapter 2
Review
mbhaub@mpsaz.org
Chapter 2 Review
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Work quickly.
Only copy what is necessary.
Use a book or notes for theorems,
definitions, postulates, but only when
really needed.
All answers on paper.
Keep track of correct & wrong answers.
22 March 2016
Geometry Chapter 2 Review
2
Conditionals
If today is Friday, then there is a football game.
Write the
1. Converse
If there is a football game, then today is Friday.
2. Inverse
If today isn’t Friday, then there isn’t a football game.
3. Contrapositive
If there isn’t a football game, then today isn’t Friday.
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Geometry Chapter 2 Review
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Biconditionals
x  5 if and only if x = 25.
4. Rewrite this statement as a conditional and its converse.
If
x  5, then x  25.
If x  25, then x  5.
22 March 2016
Geometry Chapter 2 Review
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Logic
If Mike buys a car, then he will need insurance.
Mike buys a car.
Conclusion:
He needs insurance.
5. What Law makes this a valid argument?
Law of Detachment
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Geometry Chapter 2 Review
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Law of Detachment (again)
P  Q is true.
PQ
P is true.
P
Conclusion: Q is true.
Q
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Geometry Chapter 2 Review
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Logic
If you pass the AIMS, then you will graduate.
If you graduate, then you can go to college.
6.Use the Law of Syllogism and write a
conclusion.
If you pass the AIMS, then you can go to
college.
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Geometry Chapter 2 Review
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Syllogism (again)
If P  Q, and Q  R, then P  R
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Geometry Chapter 2 Review
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Properties
7 – 12: Identify the property used.
7. 5 =5
reflexive
8. If 5 = x, then x = 5 symmetric
9. 3(x + 6) = 3x + 18 distributive
10. If x + 3 = 8, then x = 5 subtraction
11. If A  C, then mA = mC def. congruent angles
12. If MN = OP, then MN  OP def. congruent segments
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Geometry Chapter 2 Review
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Problem Solving
A
B
38
57
10x + 8
15x + 12
13. If AC = 95, find AB and BC.
C
Solution:
(10x + 8) + (15x + 12) = 95
25x + 20 = 95
25x = 75
x=3
22 March 2016
AB = 10(3) + 8 = 38
BC = 15(3) + 12 = 57
Geometry Chapter 2 Review
10
Problem Solving
14. Find m1.
52°
1 52°
Vertical Angles are Congruent
22 March 2016
Geometry Chapter 2 Review
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Problem Solving
15. Find m1.
139°
1
(3x + 20)°
41°
(5x + 6)°
5x + 6 = 3x + 20
2x = 14
x=7
3(7) + 20 = 41
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180 – 41 = 139
Geometry Chapter 2 Review
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Problem Solving
180 – 72 =
16. Find m2.
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108°
2
Geometry Chapter 2 Review
72°
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Problem Solving
17. Find the measure of each angle.
142°
38°
(8x + 30)° (2x + 10)°
Angles in a linear pair are supplementary.
(8x + 30) + (2x + 10) = 180
10x + 40 = 180
10x = 140
8(14) + 30 = 142
x = 14
2(14) + 10 = 38
22 March 2016
Geometry Chapter 2 Review
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Distance Formula
18. Find the length of the segment
between (8, 6) and (5, 4).
d  ( x2  x1 )  ( y2  y1 )
2
 (8  5)  (6  4)
2
2
2
 3 2  94
2
2
 13
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Geometry Chapter 2 Review
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Midpoint
19. Find the midpoint of the segment
between (10, –3) and (20, 17).
 10  20  3  17   30 14 
,

   ,   15,7 
2   2 2
 2
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Geometry Chapter 2 Review
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Proof
1 2
20.
Prove: 1  4
3 4
Statements
Given: 2  3
Reasons
You provide these.
1. 2  3
1. Given
2. 1 supp. 2
2. Linear Pair Post.
3. 4 supp. 3
3. Linear Pair Post.
4. 1  4
4.  supps (Th. 2.4)
QED
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Geometry Chapter 2 Review
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How did you do?
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Count up the number correct.
18 – 20: Great work. That’s an A.
16 – 17: Better than average – B.
14 – 15: Average – C.
12 – 13: Below average – D.
0 – 11: Failing. F. Need to study a lot!
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Geometry Chapter 2 Review
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Homework
Then: take time to memorize the
definitions, postulates, properties
and theorems we’ve seen so far. You
really want them in your head by test
time.
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Geometry Chapter 2 Review
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Test Tomorrow
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Study tonight: know definitions,
theorems, postulates.
Get a good night’s rest.
Have a good breakfast or lunch. Eat
brain food.
Be on time.
You will only have one period to
complete the test.
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Geometry Chapter 2 Review
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Remember…
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You may not leave the room unless you
are finished with the test.
Any cell phone use – for anything – will
result in an automatic zero.
22 March 2016
Geometry Chapter 2 Review
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22 March 2016
Geometry Chapter 2 Review
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