Triangle Congruence Shortcuts

Front

What is Triangle Congruence?

Back

Triangle congruence refers to the condition where two triangles are considered congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What are the three main Triangle Congruence Shortcuts?

Back

The three main Triangle Congruence Shortcuts are: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), 3) Angle-Side-Angle (ASA).

Front

Define Side-Side-Side (SSS) Congruence. Give an example.

Back

SSS Congruence states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. Example: Triangle ABC with sides 5, 7, 9 is congruent to Triangle DEF with sides 5, 7, 9.

Front

Define Side-Angle-Side (SAS) Congruence. Give an example.

Back

SAS Congruence 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 triangles are congruent. Example: Triangle ABC with sides 5, 7 and included angle 60° is congruent to Triangle DEF with sides 5, 7 and included angle 60°.

Front

Define Angle-Side-Angle (ASA) Congruence. Give an example.

Back

ASA Congruence 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 triangles are congruent. Example: Triangle ABC with angles 30°, 60° and included side 5 is congruent to Triangle DEF with angles 30°, 60° and included side 5.

Front

What is the Angle-Angle-Side (AAS) Congruence?

Back

AAS Congruence 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 triangles are congruent.

Front

What is the Hypotenuse-Leg (HL) Congruence?

Back

HL Congruence applies specifically to right triangles. It states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

How can you prove triangles are congruent using SSS?

Back

To prove triangles are congruent using SSS, measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent.

Front

How can you prove triangles are congruent using SAS?

Back

To prove triangles are congruent using SAS, measure two sides and the included angle of both triangles. If the two sides and the included angle are equal, the triangles are congruent.

Front

How can you prove triangles are congruent using ASA?

Back

To prove triangles are congruent using ASA, measure two angles and the included side of both triangles. If the two angles and the included side are equal, the triangles are congruent.