Proving Triangles Congruent

Front

What does it mean for two triangles to be congruent?

Back

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

Front

What are the criteria for proving triangles congruent?

Back

The main criteria are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which means if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, which means 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.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which means 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.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which means 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, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, which is a criterion used to prove the congruence of right triangles based on the equality of the hypotenuse and one leg.

Front

How can you prove triangles congruent using the AAS criterion?

Back

To prove triangles congruent using AAS, show that 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 information is needed to prove triangles congruent using ASA?

Back

To prove triangles congruent using ASA, you need two angles and the included side of one triangle to be equal to two angles and the included side of another triangle.

Front

What is the significance of congruent angles in triangles?

Back

Congruent angles in triangles indicate that the triangles may be similar or congruent, which helps in proving triangle congruence.