Proofs including triangle congruence and similarity

Front

SAS (Side-Angle-Side) Congruence

Back

A theorem stating that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

ASA (Angle-Side-Angle) Congruence

Back

A theorem stating that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front

AAS (Angle-Angle-Side) Congruence

Back

A theorem stating that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

SSS (Side-Side-Side) Congruence

Back

A theorem stating that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Front

HL (Hypotenuse-Leg) Congruence

Back

A theorem used in right triangles stating that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

Included Side

Back

The side located between two angles in a triangle.

Front

Included Angle

Back

The angle located between two sides in a triangle.

Front

CPCTC

Back

An acronym for 'Corresponding Parts of Congruent Triangles are Congruent,' used after proving triangles congruent to show that their corresponding parts are congruent.

Front

Isosceles Triangle

Back

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

-OR-

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Front

Reflexive Property of Congruence

Back

Any geometric figure is congruent to itself, often used in triangle congruence proofs when two triangles share a common side.