Proving Triangles Congruent: SSS and SAS

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a postulate that states if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a postulate that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What additional information is needed to prove triangles congruent by SSS?

Back

To prove triangles congruent by SSS, the lengths of all three sides of both triangles must be known.

Front

How can you determine if two angles are congruent?

Back

Two angles are congruent if they have the same measure.

Front

What is the importance of the included angle in the SAS postulate?

Back

The included angle is crucial in the SAS postulate because it must be between the two sides being compared for the triangles to be congruent.

Front

Can two triangles be congruent if only two sides are known?

Back

No, knowing only two sides is not sufficient to prove triangle congruence; you need either the included angle (SAS) or all three sides (SSS).

Front

What is the relationship between corresponding parts of congruent triangles?

Back

The corresponding parts of congruent triangles are equal, meaning their corresponding sides and angles are congruent.

Front

What is the Angle-Angle-Side (AAS) theorem?

Back

The AAS theorem states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the Hypotenuse-Leg (HL) theorem?

Back

The HL theorem states that in right triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, then the triangles are congruent.