2x = 10 Add 6 to each side. Addition Property of Equality = 5 Divide each side by 2. Division Property of x Equality The value of is 5. x EXAMPLE 2 Use properties of equality In the diagram, = Show that = WY XZ. WX YZ. Equation Explanation Reason Add lengths of adjacent Segment Addition WY = WX + XY segments Postulate Add lengths of adjacent Segment Addition XZ = XY + YZ segments Postulate Use given information. Given WY = XZ Substitute + for Substitution Property of WX + XY = XY + YZ WX XY WY and + for Equality XY YZ YZ. Subtract from each side. Subtraction Property of WX = YZ XY Equality LESSON 2.6 GOAL: proofs using geometric theorems. Vocabulary A proof is a logical argument that shows a statement is true. A two-column has numbered statements and corresponding reasons that show an argument in a logical order. A theorem is a statement that can be proven. Theorem 2.1 Congruence of Segments: Segment congruence is reflexive, symmetric, and transitive. Theorem 2.2 Congruence of Angles: Angle congruence is reflexive, symmetric, and transitive. EXAMPLE 1 Write a two-column proof Write a two-column proof for the following situation. GIVEN: AD = 8, BC=8,  PROVE:  Statements Reasons AD = 8 BC = 8 Given AD = BC Transitive Property of Equality Definition of congruent  segments Given 
2x = 10 Add 6 to each side. Addition Property of Equality x = 5 Divide each side by 2. Division Property of Equality The value of x is 5. EXAMPLE 2 Use properties of equality In the diagram, WY = XZ. Show that WX = YZ. Equation Explanation Reason WY = WX + XY Add lengths of adjacent segments Segment Addition Postulate XZ = XY + YZ Add lengths of adjacent segments Segment Addition Postulate WY = XZ Use given information. Given WX + XY = XY + YZ Substitute WX + XY for WY and XY + YZ for YZ. Substitution Property of Equality WX = YZ Subtract XY from each side. Subtraction Property of Equality LESSON 2.6 GOAL: proofs using geometric theorems. Vocabulary A proof is a logical argument that shows a statement is true. A two-column has numbered statements and corresponding reasons that show an argument in a logical order. A theorem is a statement that can be proven. Theorem 2.1 Congruence of Segments: Segment congruence is reflexive, symmetric, and transitive. Theorem 2.2 Congruence of Angles: Angle congruence is reflexive, symmetric, and transitive. EXAMPLE 1 Write a two-column proof Write a two-column proof for the following situation. GIVEN: AD = 8, BC=8,  PROVE:  Statements Reasons AD = 8 BC = 8 Given AD = BC Transitive Property of Equality  Definition of congruent segments  Given
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