Triangle Congruence Theorems

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What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states 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

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states 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

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem that states if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem that states if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a theorem that applies to right triangles, stating that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

How can you prove triangles are congruent using AAS?

Back

To prove triangles are congruent using AAS, show that two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle.

Front

How can you prove triangles are congruent using SAS?

Back

To prove triangles are congruent using SAS, demonstrate that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Front

How can you prove triangles are congruent using SSS?

Back

To prove triangles are congruent using SSS, establish that all three sides of one triangle are congruent to all three sides of another triangle.

Front

How can you prove triangles are congruent using ASA?

Back

To prove triangles are congruent using ASA, show that two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle.

Front

How can you prove triangles are congruent using HL?

Back

To prove triangles are congruent using HL, confirm that the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle.