Chapter 2 Section 5

Objective  Students will make a connection between reasoning in Algebra and reasoning in Geometry.

Properties of Equality  Algebraic properties of equality are used in geometry to justify steps to solving problems.

Properties of Equality Addition Property  If A = B then A + C = B + C Subtraction Property  If A = B then A – C = B – C Multiplication Property  If A = B then A · C = B · C Division Property If A = B then A ÷ C = B ÷ C (iff C ≠ 0)

Properties of Equality Reflexive Property  A = A Symmetric Property  If A = B, then B = A Transitive Property  If A = B and B = C, then A = C Substitution Property  If A = B, then A can replace B in any expression.

Distributive Property  A ( B + C ) = AB + AC

Page 114  Look at Problem 1

Properties of Congruence Reflexive, Symmetric, and Transitive properties hold true for congruence the same as they do for equivalence. (See page 114 for examples of congruence properties).

Proof  A convincing argument that uses deductive reasoning  It logically shows why a conjecture is true.

Two-column Proof  Lists each statement (or step) on the left and gives the justification on the right.

Page 116  Look at Problem 3.  Try the “Got It’ Problem 3.