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What does CPCTC stand for?

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

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What is the Angle-Side-Angle (ASA) Congruence Theorem?

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The ASA Congruence Theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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What is the Side-Angle-Side (SAS) Congruence Theorem?

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The SAS Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

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What is the Side-Side-Side (SSS) Congruence Theorem?

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

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What is the Angle-Angle-Side (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 congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

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What is the Reflexive Property in geometry?

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The Reflexive Property states that any geometric figure is congruent to itself. For example, if triangle ABC is being compared to triangle ABC, then they are congruent.

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What is the Vertical Angle Theorem?

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The Vertical Angle Theorem states that vertical angles are congruent. When two lines intersect, the angles opposite each other are equal.

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How do you identify congruent triangles?

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Congruent triangles can be identified using congruence theorems such as SSS, SAS, ASA, AAS, and HL (Hypotenuse-Leg for right triangles).

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What is the significance of corresponding parts in congruent triangles?

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In congruent triangles, corresponding parts (sides and angles) are equal, which allows us to make conclusions about the triangles' properties.

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What is the purpose of proving triangle congruence?

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Proving triangle congruence allows us to establish that two triangles are identical in shape and size, which can be used in various geometric proofs and applications.