Triangle Congruence Proofs

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What is Triangle Congruence?

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Triangle congruence refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

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What does AAS stand for in triangle congruence?

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AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and a non-included side of one triangle are equal to the corresponding parts of another triangle.

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What does SAS stand for in triangle congruence?

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SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are equal to the corresponding parts of another triangle.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are equal to the corresponding parts of another triangle.

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What does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a criterion for triangle congruence where all three sides of one triangle are equal to the corresponding sides of another triangle.

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What does CPCTC stand for?

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CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent, a principle used after proving two triangles are congruent.

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What is the SSA condition in triangle congruence?

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SSA stands for Side-Side-Angle, which is not a valid criterion for triangle congruence as it can lead to ambiguous cases.

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What is the HL criterion in triangle congruence?

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HL stands for Hypotenuse-Leg, a criterion for congruence specifically for right triangles, where the hypotenuse and one leg are equal.

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How can you prove two triangles are congruent using AAS?

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

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How can you prove two triangles are congruent using SAS?

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