Triangle Congruency Theorems

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What does ASA stand for in triangle congruence?

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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.

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What does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a theorem that states if three sides of one triangle are equal to three sides 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.

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What does HL stand for in triangle congruence?

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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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How can you prove triangles are congruent using ASA?

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

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How can you prove triangles are congruent using SSS?

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To prove triangles are congruent using SSS, you need to show that all three sides of one triangle are equal to all three sides of another triangle.

Front

How can you prove triangles are congruent using SAS?

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

Front

How can you prove triangles are congruent using AAS?

Back

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

Front

How can you prove triangles are congruent using HL?

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