Triangle Congruence Theorems

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What does SSS stand for in triangle congruence?

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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.

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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?

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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.

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What is the Hypotenuse-Leg (HL) theorem?

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The HL theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

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How can you prove triangles are congruent using SSS?

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To prove triangles are congruent using SSS, show that all three corresponding sides of the triangles are equal in length.

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How can you prove triangles are congruent using SAS?

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To prove triangles are congruent using SAS, 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 ASA?

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

Front

How can you prove triangles are congruent using AAS?

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To prove triangles are congruent using AAS, show that two angles and a non-included side of one triangle are equal to two angles and a 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 provide criteria to determine if two triangles are congruent, which is essential in solving geometric problems.