Geometry - SSS and SAS Triangle Congruence

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, then 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, then the triangles are congruent.

Front

When can you use the SSS theorem?

Back

You can use the SSS theorem when you know the lengths of all three sides of two triangles.

Front

When can you use the SAS theorem?

Back

You can use the SAS theorem when you know the lengths of two sides and the measure of the included angle of two triangles.

Front

What is the difference between SSS and SAS?

Back

SSS requires all three sides to be known, while SAS requires two sides and the included angle.

Front

What does it mean for triangles to be congruent?

Back

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

Front

Can you prove triangle congruence with just two angles?

Back

No, two angles alone do not guarantee triangle congruence; you need at least one side length (AAS or ASA) or two sides and the included angle (SAS).

Front

What is the criteria for triangle congruence using AAS?

Back

AAS stands for Angle-Angle-Side, which states that 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, then the triangles are congruent.

Front

What is the criteria for triangle congruence using ASA?

Back

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

Front

What is the importance of the included angle in SAS?

Back

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