PROPERTIES OF CONGRUENCE AND EQUALITY

A quantity is congruent or equal to itself (a = a)

Reflexive Property

The quantities on either side of a congruence (equal) sign can be interchanged.

Symmetric Property

If x = 2,then 2 = x.

Example of Symmetric Property

If ∠1 ≅ ∠2,then ∠2 ≅ ∠1.

Example of Symmetric Property

If two quantities are congruent (equal) to the same quantity, they are congruent (equal) to each other.

Transitive Property

If 2 + 3 = 5 and 5 = 1 + 4,then 2 + 3 = 1 + 4.

Example of Transitive Property

If ∠1 ≅ ∠2, and ∠2 ≅ ∠3,then∠1 ≅ ∠3.

Example of Transitive Property

If m∠1 + m∠2 = 90 and ∠2 = ∠3, then m∠1 + m∠3 = 90.

Example of Substitution Property

1 = 1

Example of Reflexive Property

AB = AB

Example of Reflexive Property

m∠1 ≅ m∠1

Example of Reflexive Property

If AB = CD,then CD = AB.

Example of Symmetric Property

If a = b, and b = c, then a = c.

Transitive Property

Contains 3 terms

Transitive Property

If a = b,then a may be substituted for b.

Substitution Property

If x = 5 and 2x = 10,then 2(5) = 10.

Example of Substitution Property

A quantity may be substituted for its equal.

Substitution Property