Proving Triangles SSS and SAS Congruent (Section 4-4)

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 equal 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 equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

Can AAA be used to prove triangle congruence?

Back

No, AAA (Angle-Angle-Angle) cannot be used to prove triangle congruence because it only shows that the triangles are similar, not necessarily 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

If two triangles have two sides equal and the included angle equal, what postulate can be used to prove congruence?

Back

The SAS (Side-Angle-Side) postulate can be used to prove congruence.

Front

If two triangles have all three sides equal, what postulate can be used to prove congruence?

Back

The SSS (Side-Side-Side) postulate can be used to prove congruence.

Front

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

Back

The included angle is the angle formed between the two sides being compared; it is crucial for establishing congruence in the SAS postulate.

Front

What is the relationship between congruence and similarity in triangles?

Back

All congruent triangles are similar, but not all similar triangles are congruent. Congruence requires equal sides and angles, while similarity only requires equal angles.

Front

How can you determine if two triangles are congruent using SSS?

Back

Measure all three sides of both triangles; if all three pairs of corresponding sides are equal, the triangles are congruent by the SSS postulate.

Front

How can you determine if two triangles are congruent using SAS?

Back

Measure two sides and the included angle of both triangles; if the two sides and the included angle are equal, the triangles are congruent by the SAS postulate.