2.5

1. PROVING STATEMENTS ABOUT SEGMENTS 2.5 1 2 GOAL GOAL Justify statements about congruent segments. Write reasons for steps in a proof Properties of congruence allow you to justify segment relationships in real life. Whatyou should learn Why you should learn it

2. PROVING STATEMENTS ABOUT SEGMENTS 2.5 PROPERTIES OF CONGRUENT SEGMENTS 1 GOAL PROPERTIES OF SEGMENT CONGRUENCE Reflexive Symmetric Transitive EXAMPLE 1 • VOCABULARY • theorem • two-column proof • paragraph proof

3. Given: EF = GH Prove: E F G H Extra Example 1 StatementsReasons 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. EF = GH Given EF + FG = GH + FG Addition Prop. of = EG = EF + FG, FH = GH + FG Segment Addition Post. EG = FH Subs. prop. of = Def. of  Segments

4. PROVING STATEMENTS ABOUT SEGMENTS 2.5 2 GOAL USING CONGRUENCE OF SEGMENTS EXAMPLE 2

5. Complete the proof. Given: Prove: R S T W X Y StatementsReasons 1. 1. Given 2. 2. 3. 3. Segment Addition Post. 4. 4. Subs. Prop. of = 5. 5. 6. 6. 7. 7. Def. of  segments EXAMPLE 3 Extra Example 2 Def. of  segments Given Subtraction Prop. of =

6. Given: X is the midpoint of Prove: XN = RX S M X R N EXAMPLE 3 Extra Example 3 StatementsReasons 1. 1. 2. 2. 3. 3. 4. 4. Given Def. of midpoint Given Transitive Prop. of =

7. Given: RS = XY, ST = WX Prove: RT = WY R S T W X Y Checkpoint StatementsReasons 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. RS = XY, ST = WX Given RS + ST = XY + WX Addition prop. of = RT = RS + ST Segment Addition Post. WY = XY + WX Segment Addition Post. RT = WY Substitution prop. of =

8. ACTIVITY Copy a Segment Construction Work through the steps on page 104 to construct a segment congruent to a given segment.

9. QUESTIONS?