Chapter 4: Congruence - Postulates and Theorems

The Distance Formula

The distance between the points P₂ (x₁, y₁) and P₂ (x₂, y₂) is the square root of (x₂ - x₁)² + (y₂ - y₁)²

Postulate 5 - The ASA (Angle Side Angle) Postulate

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent

Postulate 6 - The SAS (Side Angle Side) Postulate

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent

Corollary to The Definition of Congruent Triangles

Two triangles congruent to a third triangle are congruent to each other

Theorem 9

If two sides of a triangle are equal, the angles opposite them are equal

Corollay to Theorem 9

An equilateral triangle is equiangular

Theorem 10

If two angles of a triangle are equal, the sides opposite them are equal

Corollary to Theorem 10

An equiangular triangle is equilateral

Theorem 11 - The SSS (Side Side Side) Theorem

If the three sides of one triangle are equal to the three sides of another triangle, the triangles are congruent