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2.5 Proving Statements and Segments

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:

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2.5 Proving Statements and Segments

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  1. 2.5 Proving Statements and Segments

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

  3. Symmetric Property of Segment Congruence • Given: PQ XY • Prove: XY PQ Statements Reasons 1.PQ XY 1. Given 2.PQ = XY 2. Definition of congruent segments 3.XY = PQ 3. Symmetric property of equality 4.XY PQ 4. Definition of congruent segments P X Q Y

  4. Example

  5. Another example • Given: LK = 5, JK = 5, JK JL. • Prove: LK JL. Statements Reasons 1._________ 1. Given 2. _________ 2. Given 3. LK = JK 3. Transitive p. o. e 4. LK JK 4. ________________ 5. JK JL 5. Given 6. ________ 6. Transitive p o e LK = 5 JK = 5 Definition of congruent segments LK JL

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

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