Triangle Congruence Theorems

Front

What does the SAS (Side-Angle-Side) Congruence Postulate state?

Back

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does the AAS (Angle-Angle-Side) Congruence Theorem state?

Back

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What does the ASA (Angle-Side-Angle) Congruence Postulate state?

Back

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does the SSS (Side-Side-Side) Congruence Postulate state?

Back

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Front

Which triangle congruence theorem is not valid?

Back

SSA (Side-Side-Angle) is not a valid theorem for proving triangle congruence.

Front

What is the definition of congruent triangles?

Back

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

Front

If two triangles have two pairs of congruent angles, what can be said about the triangles?

Back

The triangles are similar, but not necessarily congruent unless the third side is also congruent.

Front

What is the significance of the included angle in the SAS postulate?

Back

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

Front

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

Back

Check if two angles and the non-included side of one triangle are congruent to the corresponding parts of the other triangle.

Front

What is the relationship between the AAA (Angle-Angle-Angle) condition and triangle congruence?

Back

AAA indicates similarity, not congruence, as it does not provide information about the sides.