2017 Algebraic and Geometric Proof 2017 Properties Addition

2017 Algebraic and Geometric Proof

2017 Properties: Addition Property of Equality If a=b, then a + c = b + c Subtraction Property of Equality Multiplication Property of Equality If a=b, then ac=bc Division Property of Equality Reflexive Property of Equality a=a Symmetric Property of Equality If a=b, then b=a Transitive Property of Equality If a=b and b=c, then a=c Substitution Property of Equality If a=b, then b can be substituted foe a in any expression

2017 New Properties: Reflexive Property of Congruence Symmetric Property of Congruence Transitive Property of Congruence Segment Addition Postulate Angle Addition Postulate AB+BC=AC

2017 Examples:

2017 Do you remember the previous postulates, theorems, and vocabulary?

2017 Using the Properties in Equations: Given Equation Subtraction Property of Equality Division Property of Equality Symmetric Property of Equality

2017 Solve this equation and write a justification for each step.

2017 Given: AB≅DE, BC ≅EF Prove: AC≅DF 1. B C D E F 1. Given 1. 1. 1. A 1.

2017 Examples: Find the angle at which the wrestling throw has the wrestler in blue’s legs are from the wrestler in red’s legs. A D B C

2017 A Examples: D B C Angle Addition Post. Substitution POE Simiplify Subtraction POE Div. POE

2017 Examples: 1 Statements 2 Reasons 1. ) Given 2. ) Def. of right angles 3. ) Trans. Prop. of =

2017 B C A Statements Reasons Given Information Def. of complementary Angles Given Information Def. of Congruent Angles Substitution Property of equality Def. of complementary Angles

2017 Homework: Geometric worksheet --- Beginning Proofs