1. Proving Statements about Segments
Section 2.5:
Proving Statements about Segments

2. Theorem – a true statement that follows as a result of other true statements. Two-column proof – has numbered statements and reasons that show the logical order of an argument. Paragraph proof – a proof written in paragraph form.

3. Theorem 2.1: Properties of Segment Congruence
Segment congruence is reflexive, symmetric, and transitive. Here are some examples: Reflexive – For any segment AB, Symmetric – If , then Transitive – If , and , then

4. Example 1:
x + 4 = 5(3x – 2)
x + 4 = 15x – 10
-14x + 4 = -10
-14x = -14
x = 1
Given
Distributive Property
Sub. Prop. of =
Div. Prop of =

5. Example 2:
4x + 3 = 9x – 12
-5x + 3 = -12
-5x = -15
x = 3
Given
Sub. Prop. of =
Div. Prop. of =

6. Example 3: Given: EF is a line segment Prove: EF EF
Statements
EF is a line segment
EF = EF
3. EF EF
Reasons
Given
Reflexive Property of Equality
Definition of congruent segments

7. HOMEWORK
pg ; 7, 8, 9,16

8. #7 Given: AB JK, JK ST Prove: AB ST
Statements
AB JK, JK ST
AB = JK, JK = ST
3. AB = ST
4. AB ST
Reasons
Given
Definition of congruent segments
Transitive Property of Equality