Triangle Congruence Theorems

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem stating that 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, a theorem stating that 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, a theorem stating that 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, a theorem stating that if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, the triangles are congruent.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

Can triangles be congruent if they do not share any sides or angles?

Back

No, triangles cannot be congruent if they do not share any sides or angles; congruence requires that all corresponding parts are equal.

Front

If two triangles have two sides of equal length and the angle between them is equal, what theorem applies?

Back

The SAS (Side-Angle-Side) theorem applies.

Front

If two triangles have two angles of equal measure and the side opposite one of the angles is equal in length, what theorem applies?

Back

The AAS (Angle-Angle-Side) theorem applies.

Front

What is the relationship between the SSS and SAS theorems?

Back

The SSS theorem can be used to prove the SAS theorem, as knowing all three sides allows you to determine the included angle.

Front

What is an example of triangles that are not congruent?

Back

Two triangles with sides measuring 3 cm, 4 cm, and 5 cm, and another triangle with sides measuring 2 cm, 3 cm, and 4 cm are not congruent.