Congruent Triangles

Front

What are congruent triangles?

Back

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

Front

What does SAS stand for in triangle congruence?

Back

Side-Angle-Side: A method to prove triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What does ASA stand for in triangle congruence?

Back

Angle-Side-Angle: A method to prove triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

What does AAS stand for in triangle congruence?

Back

Angle-Angle-Side: A method to prove triangles are congruent 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.

Front

What does SSS stand for in triangle congruence?

Back

Side-Side-Side: A method to prove triangles are congruent if all three sides of one triangle are equal to all three sides of another triangle.

Front

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

Back

Not necessarily; you need to know the included angle (SAS) or the third side (SSS) to prove congruence.

Front

What is the difference between SSA and other congruence criteria?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence because it can lead to ambiguous cases.

Front

If two triangles have two angles equal, what can be said about their sides?

Back

The sides opposite those angles are proportional, but the triangles are not necessarily congruent unless a side is also known (AAS or ASA).

Front

What is the significance of the included angle in SAS?

Back

The included angle is the angle between the two sides being compared, which is crucial for establishing congruence.

Front

How can you determine if two triangles are not congruent?

Back

If any corresponding sides or angles do not match, the triangles are not congruent.