Proving Triangles Congruent

Front

What does it mean for two triangles to be congruent?

Back

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

Front

What is the SSS Congruence Theorem?

Back

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

Front

What is the SAS Congruence Theorem?

Back

The SAS (Side-Angle-Side) Congruence Theorem 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 triangles are congruent.

Front

What is the ASA Congruence Theorem?

Back

The ASA (Angle-Side-Angle) Congruence Theorem 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 triangles are congruent.

Front

What is the AAS Congruence Theorem?

Back

The AAS (Angle-Angle-Side) Congruence 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 triangles are congruent.

Front

What is the definition of AAA in triangle congruence?

Back

AAA (Angle-Angle-Angle) indicates that all three angles of one triangle are equal to all three angles of another triangle, but it does not prove congruence as it does not guarantee equal side lengths.

Front

How can you determine if two triangles are not congruent?

Back

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

Front

What is the importance of the included angle in SAS?

Back

In SAS, the included angle is crucial because it is the angle formed between the two sides being compared, which helps establish congruence.

Front

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

Back

No, at least two sides and the included angle or two angles and a side must be known to determine congruence.

Front

What does 'Cannot Be Determined' mean in triangle congruence?

Back

'Cannot Be Determined' means there is insufficient information to conclude whether the triangles are congruent or not.