September 12th Triangle Congruence 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 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 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 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?

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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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When can you use the SAS theorem?

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You can use the SAS theorem when you know two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

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When can you use the SSS theorem?

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You can use the SSS theorem when you know all three sides of one triangle are equal to all three sides of another triangle.

Front

When can you use the ASA theorem?

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You can use the ASA theorem when you know two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

When can you use the AAS theorem?

Back

You can use the AAS theorem when you know two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

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What is the significance of triangle congruence theorems?

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Triangle congruence theorems are significant because they allow us to prove that two triangles are identical in shape and size, which is essential in various geometric proofs and applications.