Triangle Congruence

Front

What is a triangle?

Back

A triangle is a three-sided polygon formed by connecting three points (vertices) with straight lines (sides).

Front

What does it mean for triangles to be congruent?

Back

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

Front

What are the three main criteria for triangle congruence?

Back

1. Side-Side-Side (SSS) Congruence: All three sides of one triangle are equal to the three sides of another triangle. 2. Side-Angle-Side (SAS) Congruence: Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle. 3. Angle-Side-Angle (ASA) Congruence: Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

What is the Side-Side-Side (SSS) Congruence Postulate?

Back

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

Front

What is the Side-Angle-Side (SAS) Congruence Postulate?

Back

The SAS Congruence 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.

Front

What is the Angle-Side-Angle (ASA) Congruence Postulate?

Back

The ASA Congruence 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.

Front

What is the Angle-Angle-Side (AAS) Congruence Theorem?

Back

The AAS Congruence 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 importance of triangle congruence in geometry?

Back

Triangle congruence is important in geometry because it allows us to determine that two triangles are identical in shape and size, which is essential for solving problems related to measurements, constructions, and proofs.

Front

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

Back

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

Front

What is a corresponding part in triangle congruence?

Back

Corresponding parts in triangle congruence refer to the sides and angles of two triangles that are equal to each other when the triangles are congruent.