2.5 PROVING STATEMENTS ABOUT SEGMENTS GOAL 1 Justify statements about congruent segments. GOAL 2 Write reasons for steps in a proof What you should learn.

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Presentation transcript:

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

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

Extra Example 1 Given: EF = GH Prove: EFGH StatementsReasons EF = GHGiven EF + FG = GH + FGAddition Prop. of = EG = EF + FG, FH = GH + FG Segment Addition Post. EG = FHSubs. prop. of = Def. of  Segments

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

Extra Example 2 EXAMPLE 3 StatementsReasons Given Segment Addition Post Subs. Prop. of = Def. of  segments Def. of  segments Given Subtraction Prop. of = Complete the proof. Given: Prove: RST WXY

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

Checkpoint StatementsReasons Given: RS = XY, ST = WX Prove: RT = WY RST WXY RS = XY, ST = WX Given RS + ST = XY + WX Addition prop. of = RT = RS + STSegment Addition Post. WY = XY + WXSegment Addition Post. RT = WYSubstitution prop. of =

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

QUESTIONS?