Triangle Congruence

Front

What is the SSS Postulate?

Back

The SSS (Side-Side-Side) Postulate states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What is the SAS Postulate?

Back

The SAS (Side-Angle-Side) Postulate states 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 two triangles are congruent.

Front

What is the ASA Postulate?

Back

The ASA (Angle-Side-Angle) Postulate states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What is the AAS Theorem?

Back

The AAS (Angle-Angle-Side) Theorem 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 two triangles are congruent.

Front

What does it mean for triangles to be congruent?

Back

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

Front

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

Back

No, knowing only one side is not sufficient to determine congruence; at least two sides and the included angle or two angles and a side must be known.

Front

What is the importance of the included angle in the SAS Postulate?

Back

The included angle is crucial in the SAS Postulate because it ensures that the two triangles are positioned in the same way, allowing for congruence.

Front

How can you prove two triangles are congruent using the SSS Postulate?

Back

To prove two triangles are congruent using the SSS Postulate, measure all three sides of both triangles and show that they are equal.

Front

What is a counterexample in the context of triangle congruence?

Back

A counterexample is a specific case that shows that a certain statement is false; for example, two triangles with two equal sides but different angles are not congruent.

Front

What is the relationship between congruence and similarity in triangles?

Back

Congruent triangles are similar, but similar triangles are not necessarily congruent; similarity means they have the same shape but may differ in size.