Download Algebraic Properties of Equality

Geometry 2.5
Big Idea: Reason
Using Properties from
Algebra
Algebraic Properties of
Equality
Addition Property
If a = b, then a + c = b + c
Subtraction Property
If a = b, then a - c = b – c
(This is what we do when we solve
equations.)
Multiplication Property
If a = b, then ac = bc
Division Property
If a = b and c ≠ 0,
then a = b
c
c
Substitution Property
If a = b, then ‘a’ can be
substituted for ‘b’ in any
equation. (and vice-versa)
Distributive Property
a(b + c) = ab + ac
Reflexive Property of Equality
Real Numbers:
a=a
Segment Length: AB = AB
Angle Measure: m A = m A
Symmetric Property of Equality
Real Numbers: if a = b, then b = a
Segment Length: if AB = CD,
then CD = AB
Angle Measure: if m A = m B,
then m B = m A,
Transitive Property of Equality
Real Numbers: if a = b and b = c,
then a = c
Segment Length: if AB = CD and
CD = EF, then AB = EF
Angle Measure: if m A = m B
and m B = m C, then m A=m C
Example: Solve. Write a reason for
each step.
2x + 5 = 20 - 3x
Given
5x + 5 = 20
5x = 15
Add. Prop. Of Eq.
x=3
Div. Prop. Of Eq.
Sub. Prop. Of Eq.
Example: Solve. Write a reason for
each step.
-4 (11x + 2) = 80