Triangle Congruency Theorems

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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 equal to two angles and the 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 equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

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 equal to two angles and the corresponding non-included side 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 equal to all three sides of another triangle, then the triangles are congruent.

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

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When can the ASA theorem be applied?

Back

The ASA theorem can be applied when two angles and the included side of one triangle are known to be equal to two angles and the included side of another triangle.

Front

When can the SAS theorem be applied?

Back

The SAS theorem can be applied when two sides and the included angle of one triangle are known to be equal to two sides and the included angle of another triangle.

Front

When can the AAS theorem be applied?

Back

The AAS theorem can be applied when two angles and a non-included side of one triangle are known to be equal to two angles and the corresponding non-included side of another triangle.

Front

When can the SSS theorem be applied?

Back

The SSS theorem can be applied when all three sides of one triangle are known to be equal to all three sides of another triangle.

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When can the HL theorem be applied?

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The HL theorem can be applied specifically to right triangles when the hypotenuse and one leg of one triangle are known to be equal to the hypotenuse and one leg of another triangle.