SSS and SAS

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which is a triangle congruence 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, which is a triangle congruence 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 is the included angle in the SAS theorem?

Back

The included angle in the SAS theorem is the angle formed between the two sides that are being considered for congruence.

Front

Can two triangles be congruent if only one side is known?

Back

No, two triangles cannot be proven congruent with only one side known; additional information about angles or other sides is needed.

Front

What is the significance of the order of sides and angles in SAS?

Back

In SAS, the order matters because the angle must be between the two sides being compared for the triangles to be congruent.

Front

True or False: The SSS theorem can be used if only two sides are known. Why?

Back

False. The SSS theorem requires all three sides to be known to prove triangle congruence.

Front

What is a common misconception about triangle congruence?

Back

A common misconception is that knowing two angles is sufficient to prove triangle congruence, which is only true if the third side is also known (Angle-Angle-Side theorem).

Front

What is the Angle-Angle-Angle (AAA) criterion?

Back

The AAA criterion states that if two triangles have equal corresponding angles, they are similar but not necessarily congruent.

Front

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

Back

To determine if two triangles are congruent using the SAS theorem, check if two sides of one triangle are equal to two sides of the other triangle and that the included angle is also equal.

Front

What is the relationship between congruence and similarity in triangles?

Back

Congruent triangles are similar, but similar triangles are not necessarily congruent; similarity only requires equal angles and proportional sides.