Triangle Congruence

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What is Triangle Congruence?

Back

Triangle congruence means that two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

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What does the H-L Theorem state?

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The Hypotenuse-Leg (H-L) 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 two triangles are congruent.

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What does AAS stand for in triangle congruence?

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AAS stands for Angle-Angle-Side, a method to prove triangle congruence where two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

Front

What does ASA stand for in triangle congruence?

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ASA stands for Angle-Side-Angle, a method to prove triangle congruence where two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a method to prove triangle congruence where two sides and the included angle of one triangle are equal to two sides and the corresponding included angle of another triangle.

Front

What does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a method to prove triangle congruence where all three sides of one triangle are equal to all three sides of another triangle.

Front

What is the SSA condition in triangle congruence?

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The SSA condition (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

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How can you prove two triangles are congruent using AAS?

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To prove two triangles are congruent using AAS, show that two angles and a non-included side of one triangle are equal to the corresponding two angles and the non-included side of the other triangle.

Front

How can you prove two triangles are congruent using SAS?

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To prove two triangles are congruent using SAS, show that two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of the other triangle.

Front

How can you prove two triangles are congruent using ASA?

Back

To prove two triangles are congruent using ASA, show that two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle.