Triangle Congruence Proofs with CPCTC

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What is CPCTC?

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CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent'. It is used after proving two triangles are congruent to state that their corresponding parts are also congruent.

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What does SSS stand for in triangle congruence?

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SSS stands for 'Side-Side-Side'. It is a criterion for triangle congruence that states if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

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What does SAS stand for in triangle congruence?

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SAS stands for 'Side-Angle-Side'. It is a criterion for triangle congruence 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.

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What does ASA stand for in triangle congruence?

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ASA stands for 'Angle-Side-Angle'. It is a criterion for triangle congruence 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 AAS stand for in triangle congruence?

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AAS stands for 'Angle-Angle-Side'. It is a criterion for triangle congruence that states 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, then the triangles are congruent.

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What are vertical angles?

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Vertical angles are the angles opposite each other when two lines cross. They are always congruent.

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State the definition of congruent triangles.

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Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

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What is the significance of proving triangles congruent?

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Proving triangles congruent allows us to conclude that their corresponding parts (sides and angles) are also congruent, which is essential in solving many geometric problems.

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What is the purpose of a proof in geometry?

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The purpose of a proof in geometry is to provide a logical argument that establishes the truth of a statement or theorem based on previously established statements, definitions, and axioms.

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What is a corresponding part in triangle congruence?

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A corresponding part in triangle congruence refers to the sides or angles of one triangle that match with the sides or angles of another triangle after they have been proven congruent.