Triangle Congruence

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What is a triangle?

Back

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

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What does it mean for triangles to be congruent?

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Triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

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What are the three main triangle congruence theorems?

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1. SSS (Side-Side-Side) Theorem: If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. 2. SAS (Side-Angle-Side) Theorem: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. 3. ASA (Angle-Side-Angle) Theorem: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

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What is the SSS Congruence Theorem?

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The SSS Congruence Theorem 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 is the SAS Congruence Theorem?

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The SAS Congruence Theorem 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 is the ASA Congruence Theorem?

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The ASA Congruence Theorem 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 is the 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 equal to two angles and a corresponding non-included side of another triangle, then the triangles are congruent.

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What is the HL Congruence Theorem?

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The HL Congruence Theorem states that if a right triangle has one leg and the hypotenuse equal to the corresponding leg and hypotenuse of another right triangle, then the triangles are congruent.

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

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