REASONING IN ALGEBRA AND GEOMETRY

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 PropertyIf 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.