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Geometry
Chapter 2 Review
mbhaub@mpsaz.org
April 10, 2023 Geometry Chapter 2 Review 2
Chapter 2 Review 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.
April 10, 2023 Geometry Chapter 2 Review 3
ConditionalsIf today is Friday, then there is a football game.Write the
1. Converse
2. Inverse
3. Contrapositive
If there is a football game, then today is Friday.
If today isn’t Friday, then there isn’t a football game.
If there isn’t a football game, then today isn’t Friday.
April 10, 2023 Geometry Chapter 2 Review 4
Biconditionals
5x if and only if x = 25.
4. Rewrite this statement as a conditional and its converse.
5.x then 25, x If
25. x then x If
,5
April 10, 2023 Geometry Chapter 2 Review 5
LogicIf 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
April 10, 2023 Geometry Chapter 2 Review 6
Law of Detachment (again)
P Q is true.
P is true.
Conclusion: Q is true.
P Q
P
Q
April 10, 2023 Geometry Chapter 2 Review 7
LogicIf 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.
April 10, 2023 Geometry Chapter 2 Review 8
Syllogism (again)
If P Q, and Q R, then P R
April 10, 2023 Geometry Chapter 2 Review 9
Properties7 – 12: Identify the property used.
7. 5 =5
8. If 5 = x, then x = 5
9. 3(x + 6) = 3x + 18
10. If x + 3 = 8, then x = 5
11. If A C, then mA = mC
12. If MN = OP, then OPMN
reflexive
symmetric
distributive
subtraction
def. congruent angles
def. congruent segments
April 10, 2023 Geometry Chapter 2 Review 10
Problem SolvingA B C
10x + 8 15x + 1213. If AC = 95, find AB and BC.
Solution:
(10x + 8) + (15x + 12) = 95
25x + 20 = 95
25x = 75
x = 3
AB = 10(3) + 8 = 38
BC = 15(3) + 12 = 57
38 57
April 10, 2023 Geometry Chapter 2 Review 11
Problem Solving
52° 114. Find m1. 52°
Vertical Angles are Congruent
April 10, 2023 Geometry Chapter 2 Review 12
Problem Solving
(3x + 20)° (5x + 6)°1
15. Find m1.
5x + 6 = 3x + 20
2x = 14
x = 7
3(7) + 20 = 41
41°
180 – 41 = 139
139°
April 10, 2023 Geometry Chapter 2 Review 13
Problem Solving
2 72°
16. Find m2.
180 – 72 =
108°
April 10, 2023 Geometry Chapter 2 Review 14
Problem Solving
(2x + 10)°(8x + 30)°
17. Find the measure of each angle.
Angles in a linear pair are supplementary.
(8x + 30) + (2x + 10) = 180
10x + 40 = 180
10x = 140
x = 14
8(14) + 30 = 142
2(14) + 10 = 38
142° 38°
April 10, 2023 Geometry Chapter 2 Review 15
Distance Formula18. Find the length of the segment between (8, 6) and (5, 4).
13
4923
)46()58(
)()(
22
22
212
212
yyxxd
April 10, 2023 Geometry Chapter 2 Review 16
Midpoint19. Find the midpoint of the
segment between (10, –3) and (20, 17).
7,152
14,
2
30
2
173,
2
2010
April 10, 2023 Geometry Chapter 2 Review 17
Proof21
3 4
20. Given: 2 3
Prove: 1 4
Statements Reasons
1. 2 3
2. 1 supp. 2
3. 4 supp. 3
4. 1 4
QED
You provide these.
1. Given
2. Linear Pair Post.
3. Linear Pair Post.
4. supps (Th. 2.4)
April 10, 2023 Geometry Chapter 2 Review 18
How did you do? 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!
April 10, 2023 Geometry Chapter 2 Review 19
HomeworkThen: 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.
April 10, 2023 Geometry Chapter 2 Review 20
Test Tomorrow 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.
April 10, 2023 Geometry Chapter 2 Review 21
Remember… 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.
April 10, 2023 Geometry Chapter 2 Review 22