2.5 Proving Statements and Segments. Properties of Segment Congruence Segment congruence is reflexive, symmetric, and transitive. Reflexive: For any segment.

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2.5 Proving Statements and Segments

Properties of Segment Congruence Segment congruence is reflexive, symmetric, and transitive. Reflexive: For any segment AB,. Symmetric: If, then. Transitive: If, and, then

Symmetric Property of Segment Congruence Given: PQ XY Prove: XY PQ StatementsReasons 1.PQ XY1. Given 2.PQ = XY2. Definition of congruent segments 3.XY = PQ3. Symmetric property of equality 4.XY PQ 4. Definition of congruent segments X Y P Q

Example

Another example Given: LK = 5, JK = 5, JK JL. Prove: LK JL. StatementsReasons 1._________ 1. Given 2. _________2. Given 3. LK = JK3. Transitive p. o. e 4. LK JK4. ________________ 5. JK JL5. Given 6. ________6. Transitive p o e LK = 5 JK = 5 Definition of congruent segments LK JL

Solve for the variable using the given information. Explain your steps. Given: A BC D.... 2X + 1 4X - 11