Triangle Congruence Theorems

Front

What is the AAS (Angle-Angle-Side) Congruence Theorem?

Back

The AAS Congruence Theorem states that if two angles and the non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Front

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

Back

The SAS Congruence Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

Define the SSS (Side-Side-Side) Congruence Postulate.

Back

The SSS Congruence Postulate states that if all three sides of one triangle are congruent to all three sides of another triangle, then the two triangles are congruent.

Front

What is the ASA (Angle-Side-Angle) Congruence Theorem?

Back

The ASA Congruence Theorem states that if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the two triangles are congruent.

Front

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

Back

To determine if two triangles are congruent using the AAS theorem, you need to show that two angles and the non-included side of one triangle are congruent to the corresponding two angles and the non-included side of the other triangle.

Front

What additional information is needed for two triangles to be congruent by AAS?

Back

To use the AAS theorem, you need two angles and one non-included side of one triangle to be congruent to the corresponding parts of the other triangle.

Front

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

Back

In the SAS postulate, the included angle is the angle formed between the two sides being compared. It is crucial because it directly affects the congruence of the triangles.

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 non-included side are needed.

Front

What does it mean for triangles to be congruent?

Back

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

Front

If two triangles have two pairs of congruent angles, what can be concluded?

Back

If two triangles have two pairs of congruent angles, they are congruent by the AAS theorem.