SSS, SAS, ASA, and AAS Triangle Congruence

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which states that 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, which states that 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 does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which 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

Can triangles be congruent by AAA?

Back

No, AAA (Angle-Angle-Angle) does not guarantee triangle congruence, as it only shows that the triangles are similar, not necessarily congruent.

Front

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

Back

You need to know that the lengths of the two sides that are not included are congruent.

Front

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

Back

You need to know that the lengths of the sides opposite the given angles are congruent.

Front

If two triangles have two pairs of congruent angles, what can be concluded?

Back

The triangles are similar, but not necessarily congruent unless the sides are also known.

Front

What is the significance of the included angle in SAS?

Back

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

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 sides are congruent, the triangles are congruent.