Proving Triangles Congruent

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent.

Front

What is the SAS theorem in triangle congruence?

Back

SAS stands for Side-Angle-Side, which 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 triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem that states 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 is the significance of vertical angles in triangle congruence?

Back

Vertical angles are always congruent, which can be used to establish congruence in triangles when applying the ASA or AAS theorems.

Front

Which triangle congruence theorem is not valid?

Back

SSA (Side-Side-Angle) is not a valid triangle congruence theorem because it does not guarantee that two triangles are congruent.

Front

What is the definition of congruent triangles?

Back

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

Front

How can you prove triangles are congruent using the AAS theorem?

Back

To prove triangles are congruent using AAS, you need to show that two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle.

Front

What information is needed to apply the SAS theorem?

Back

To apply the SAS theorem, you need to know the lengths of two sides and the measure of the included angle of one triangle compared to another triangle.

Front

What is the relationship between the angles in congruent triangles?

Back

In congruent triangles, corresponding angles are equal, meaning if two triangles are congruent, their angles match in measure.

Front

What is the purpose of triangle congruence theorems?

Back

Triangle congruence theorems are used to determine whether two triangles are congruent based on their sides and angles, which is essential in solving geometric problems.