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