1. Chapter 2 Review
Reasoning and Proof

2. Theorems are accepted as true.
Vocab:State whether each sentence is true or false. If false, replace the incorrect word to make it true.
Theorems are accepted as true.
In a two-column proof, the properties that justify each step are called reasons.
The Reflexive Property of Equality states that for any number a, a=a.
The contrapositive of a conditional is formed by switching the hypothesis and conclusion of the original statement.

3. X, Y and Z are collinear and XY = YZ
Inductive Reasoning and Conjecture: Make a conjecture based on the given information. Draw a figure if necessary.
and are supplementary
X, Y and Z are collinear and XY = YZ

4. The intersection of two planes is a line.
Conditional Statements: a)Write each statement in if-then form, then identify the hypothesis and conclusion. b)Write the converse of the statement. If it is false give a counterexample.
March has 31 days.
The intersection of two planes is a line.

5. The intersection of two different lines is a line.
Postulates:Determine if each statement is always, sometimes, or never true. Explain.(use a postulate or theorem to explain when possible)
The intersection of two different lines is a line.
If P is the midpoint of XY, then XP=PY.
Four points determine exactly one plane.
If MX = MY, then M is the midpoint of XY.

6. If 3 = CD, and CD=XY, then 3 = XY
Algebraic Properties and Proof: State the property that justifies each statement.
If 3(x +2)=6, then 3x+6= 6
If 10x = 20, then x = 2
If AB + 20 = 45, then AB = 25
If 3 = CD, and CD=XY, then 3 = XY

7. Algebraic Proof: Write a two-column proof.
If AC = AB, AC = 4x+1 and AB = 6x-13, then x = 7.

8. Proving Segment Relationship: Write a two-column proof
Given: AB=CD
Prove: AC = BD A B C D

9. Angle Relationship: Find the measure of the numbered angle2 3 73 1 C B E

10. Proving Angle Relationships: Write a two-column proof
Given:
Prove: E C A B

11. ANSWERS Slide 1: 1. Postulates are accepted as true. 2. True 3. True
4. The converse of a conditional is formed by switching the hypothesis and conclusion of the original statement.

12. ANSWERS Slide 2: 1. Angles A and B are a linear pair.
2. Y is the midpoint of XZ.

13. ANSWERS Slide 3: 1. a) If it is March, then the month has 31 days.
- hyp- It is March concl.- the month has 31 days
b) If the month has 31 days, then it is March.
-false= There are 31 days in the month of July
a) If two planes intersect, then the intersection is a line.
-hyp- two planes intersect concl.- it is a line
b) If the intersection is a line, then two planes intersected.
-true

14. ANSWERS
Slide 4:
1. Never, because the intersection of two lines is exactly one point.
2. Always, that is the definition of a midpoint.
3. Sometimes, because 3 points determine exactly one plane, the fourth point could be on a second plane.
4. Sometimes, X and Y could be collinear so the lines with X and Y would be intersecting at M and therefore M would not be a midpoint.

15. ANSWERS Slide 5: 1. Distributive Property 2. Division Property
3. Subtraction Property
4. Transitive Property

16. ANSWERS Given: AC = AB, AC = 4x + 1, AB = 6x – 13 Prove: x = 7
AC = AB, AC = 4x + 1, 1. Given
AB = 6x – 13
4x + 1 = 6x – Substitution Prop
4x + 1 – 4x= 6x – 13 – 4x 3. Subtraction Prop
1 = 2x – Substitution Prop
= 2x – Addition Prop
14 = 2x Substitution Prop
14/2 = 2x/ Division Prop
7 = x Substitution Prop
x = Symmetric Prop

17. ANSWERS Slide 7: AB = CD 1. Given
AB + BC = AC 2. Segment Addition Postulate
BC + CD = BD
CD + BC = AC 3. Substitution Prop
AC = BD 4. Substitution Prop
Given: AB = CD
Prove: AC = BD A B C D

18. ANSWERS Slide 8: 1. angle 1 + 73 = 90 angle 1 = 17
2. perpendicular lines =rt angles angle2 = 90
3. angles 2 and 3 are vertical angles. Vertical angles are congruent. angle 3= 90

19. ANSWERS Given: Prove: 3. ABE + EBF = ABF 3. Angle Addition PostulateC E
Given:
Prove: A B
ABF is congruent to EBC 1. Given
ABF = EBC 2. Definition of congruent angles
3. ABE + EBF = ABF 3. Angle Addition Postulate
EBF + FBC = EBC
4. ABE + EBF = EBF + FBC 4. Substitution Prop
5. ABE + EBF – EBF = 5. Subtraction Prop
EBF + FBC - EBF
6. ABE = FBC 6. Substitution Prop
*Angle symbols should be used in front of each set of 3 letters