Triangle Congruence Theorems

Front

What does the ASA postulate state?

Back

The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What does the AAS postulate state?

Back

The AAS (Angle-Angle-Side) postulate states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Front

What does the SSS postulate state?

Back

The SSS (Side-Side-Side) postulate states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What does the SAS postulate state?

Back

The SAS (Side-Angle-Side) postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What does the HL theorem state?

Back

The HL (Hypotenuse-Leg) theorem states that in right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the two triangles are congruent.

Front

Example of ASA postulate: If ∠A = ∠D, ∠B = ∠E, and AB = DE, what can be concluded?

Back

Triangles ABC and DEF are congruent by the ASA postulate.

Front

Example of AAS postulate: If ∠A = ∠D, ∠B = ∠E, and AC = DF, what can be concluded?

Back

Triangles ABC and DEF are congruent by the AAS postulate.

Front

Example of SSS postulate: If AB = DE, BC = EF, and AC = DF, what can be concluded?

Back

Triangles ABC and DEF are congruent by the SSS postulate.

Front

Example of SAS postulate: If AB = DE, ∠C = ∠F, and AC = DF, what can be concluded?

Back

Triangles ABC and DEF are congruent by the SAS postulate.

Front

Example of HL theorem: If hypotenuse AB = DE and leg AC = DF, what can be concluded?

Back

Right triangles ABC and DEF are congruent by the HL theorem.