Triangle Congruence

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What does the SSS Postulate state?

Back

The SSS (Side-Side-Side) 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 does the SAS Postulate state?

Back

The SAS (Side-Angle-Side) 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 two triangles are congruent.

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What does the ASA Postulate state?

Back

The ASA (Angle-Side-Angle) 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 two triangles are congruent.

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What does the AAS Theorem state?

Back

The AAS (Angle-Angle-Side) 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 two triangles are congruent.

Front

What is the definition of congruent triangles?

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

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How can you prove triangles are congruent using the SSS Postulate?

Back

To prove triangles are congruent using the SSS Postulate, you must show that all three sides of one triangle are equal to the three sides of another triangle.

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How can you prove triangles are congruent using the SAS Postulate?

Back

To prove triangles are congruent using the SAS Postulate, you must show that two sides and the angle between them in one triangle are equal to the corresponding two sides and angle in another triangle.

Front

How can you prove triangles are congruent using the ASA Postulate?

Back

To prove triangles are congruent using the ASA Postulate, you must show that two angles and the side between them in one triangle are equal to the corresponding two angles and side in another triangle.

Front

How can you prove triangles are congruent using the AAS Theorem?

Back

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

Front

What is the importance of triangle congruence in geometry?

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Triangle congruence is important in geometry because it allows us to determine that two triangles are identical in shape and size, which is fundamental in solving various geometric problems.