Triangle Congruence Theorems

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What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem used to prove that two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem used to prove that two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem used to prove that two triangles are congruent 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.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem used to prove that two triangles are congruent if all three sides of one triangle are equal to all three sides of another triangle.

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What are congruent figures?

Back

Congruent figures are figures that have the same dimensions (side lengths and angle measures), are the same shape and size, and can be mapped onto one another using rigid motions.

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How do you name a triangle congruent to triangle ABC if the corresponding vertices are F, M, and N?

Back

The triangle congruent to triangle ABC would be named triangle FMN.

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How do you name a triangle congruent to triangle XYZ if the corresponding vertices are X, W, and Z?

Back

The triangle congruent to triangle XYZ would be named triangle XWZ.

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What is the purpose of triangle congruence theorems?

Back

The purpose of triangle congruence theorems is to determine whether two triangles are congruent based on their sides and angles.

Front

What is the difference between congruent triangles and similar triangles?

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Congruent triangles have the same size and shape (equal sides and angles), while similar triangles have the same shape but not necessarily the same size (proportional sides and equal angles).

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What is the Angle-Angle (AA) criterion for triangle similarity?

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The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.