Triangle Proofs and CPCTC

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What is CPCTC?

Back

CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent'. It is used after proving that two triangles are congruent to conclude that their corresponding parts are also 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 postulate that states if two sides and the included angle of one triangle are congruent 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?

Back

ASA stands for 'Angle-Side-Angle'. It is a postulate that states if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does SSS stand for in triangle congruence?

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

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What does HL stand for in triangle congruence?

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HL stands for 'Hypotenuse-Leg'. It is a theorem that applies to right triangles, stating that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

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Can triangles be congruent if they have the same angles but different side lengths?

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No, triangles cannot be congruent if they have the same angles but different side lengths. This is known as the AAA (Angle-Angle-Angle) condition, which does not guarantee congruence.

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When can CPCTC be applied?

Back

CPCTC can be applied after two triangles have been proven to be congruent using one of the congruence postulates (SAS, ASA, SSS, or HL).

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What is the significance of the 'Given' statement in triangle proofs?

Back

The 'Given' statement provides the initial information or conditions that are accepted as true and serve as the starting point for the proof.

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What is the purpose of a triangle proof?

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The purpose of a triangle proof is to demonstrate that two triangles are congruent by logically deducing relationships between their sides and angles.

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What is the difference between congruence and similarity in triangles?

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Congruence means that two triangles are identical in shape and size (all corresponding sides and angles are equal), while similarity means that two triangles have the same shape but may differ in size (corresponding angles are equal, but sides are proportional).