Study Guide - Triangle Congruence Postulates

Side-Side-Side (SSS) Postulate

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

Side-Angle-Side (SAS) Postulate

If two sides and the angle between them of one triangle are equal to two sides and the angle between them of another triangle, then the triangles are congruent.

Angle-Side-Angle (ASA) Postulate

If two angles and the side between them of one triangle are equal to two angles and the side between them of another triangle, then the triangles are congruent.

Angle-Angle-Side (AAS) Theorem

If two angles and a non-included side of one triangle are equal to two angles and the corresponding side of another triangle, then the triangles are congruent.

Hypotenuse-Leg (HL) Theorem

If the hypotenuse and a leg of one right triangle are equal to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

Triangle Congruence

Triangles are congruent if they are identical in shape and size.

Congruent Triangles

Triangles that can be superimposed on each other, covering each other perfectly.

Order of Vertices

The sequence in which the vertices of the triangles are labeled is crucial in determining congruency.

Application of Congruence Postulates

Essential for solving geometric problems, proofs, and constructing geometric figures.

Importance of Angles and Sides in Congruence

The angles and sides of triangles are critical for determining whether triangles are congruent.