Triangle Congruence Proofs Including CPCTC

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What is Triangle Congruence?

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Triangle Congruence refers to the condition where two triangles are considered congruent if their corresponding sides and angles are equal.

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What does CPCTC stand for?

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CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent', which is used to prove that corresponding sides and angles of congruent triangles are equal.

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What is the Reflexive Property in geometry?

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What are the criteria for triangle congruence?

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The criteria for triangle congruence include: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

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What is the SSS Congruence Postulate?

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The SSS Congruence Postulate states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

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What is the SAS Congruence Postulate?

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The SAS Congruence Postulate states that 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 is the ASA Congruence Postulate?

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The ASA Congruence Postulate states that 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 is the AAS Congruence Theorem?

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The AAS Congruence Theorem states that 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.

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What is the HL Congruence Theorem?

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The HL Congruence 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, then the triangles are congruent.

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What is the importance of vertical angles in triangle congruence?

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Vertical angles are always congruent, which can be used as a reason in proofs involving triangle congruence.