Triangle Congruence Theorems

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What does SSS stand for in triangle congruence?

Back

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

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

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What does ASA stand for in triangle congruence?

Back

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

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem stating that if two angles and a non-included side of one triangle are equal to two angles and a corresponding non-included side of another triangle, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

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HL stands for Hypotenuse-Leg, a theorem applicable 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, the triangles are congruent.

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What is the AAA criterion in triangle congruence?

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AAA stands for Angle-Angle-Angle, which states that if three angles of one triangle are equal to three angles of another triangle, the triangles are similar but not necessarily congruent.

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When can you use the SSS theorem?

Back

You can use the SSS theorem when you know the lengths of all three sides of two triangles and want to prove they 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.

Front

When can you use the ASA theorem?

Back

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 a corresponding non-included side of another triangle.