Triangle Congruence

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What is Triangle Congruence?

Back

Triangle congruence refers to the condition where two triangles are considered congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

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What are the criteria for triangle congruence?

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The criteria for triangle congruence are: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), 3) Angle-Side-Angle (ASA), 4) Angle-Angle-Side (AAS), and 5) Hypotenuse-Leg (HL) for right triangles.

Front

Define Side-Side-Side (SSS) Congruence.

Back

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

Front

Define Side-Angle-Side (SAS) Congruence.

Back

SAS Congruence 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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Define Angle-Side-Angle (ASA) Congruence.

Back

ASA Congruence 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.

Front

Define Angle-Angle-Side (AAS) Congruence.

Back

AAS Congruence 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.

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What is Hypotenuse-Leg (HL) Congruence?

Back

HL Congruence applies to right triangles and states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

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What is the importance of triangle congruence in geometry?

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Triangle congruence is important in geometry as it helps in proving the properties of triangles, solving problems related to triangle measurements, and establishing relationships between different geometric figures.

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How can you prove that two triangles are congruent using SSS?

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To prove two triangles are congruent using SSS, measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent.

Front

How can you prove that two triangles are congruent using SAS?

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To prove two triangles are congruent using SAS, measure two sides and the included angle of both triangles. If the two sides and the included angle are equal, the triangles are congruent.