1

2-4 Reasoning in Algebra

Objectives:

• Use basic properties of algebra in reasoning

• Define congruence

• State the properties of congruence

2

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 and c ≠ 0, then a/c = b/c

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 b can replace a in any expression

Distributive Property a(b + c) = ab + ac

3

Solve and Write a Justification for Each Step

2 (x + 1) = 8 Given

2x + 2 = 8 Distributive Property

2x = 6 Subtraction Property of =

x = 3 Division Property of =

4

Congruence in Geometry

• Congruence – Having the same shape and size

• Symbol for congruence ≅• AB ≅ CD (Segment AB is congruent

to segment CD.)

A B C D

•∠ A ≅ ∠ B (Angle A is congruent to angle B.)

A B

5

Properties of Congruence

• Reflexive Property

AB ≅ AB ∠ A ≅ ∠ A• Symmetric Property

If AB ≅ CD, then CD ≅ AB If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A• Transitive Property

If AB ≅ CD and CD ≅ EF, then AB ≅ EF If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C,then ∠ A ≅

∠ C