Triangle Congruence Theorems

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states 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 SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states 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 SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem that states if all three sides of one triangle are congruent to all three sides 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 corresponding included side of another triangle, then the triangles are congruent.

Front

What is the significance of the SSA condition in triangle congruence?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

How can you prove triangles are congruent using AAS?

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 additional information is needed to prove triangles are congruent by ASA?

Back

To prove triangles are congruent by ASA, you need to know two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle.

Front

Can AAA be used to prove triangle congruence?

Back

No, AAA (Angle-Angle-Angle) cannot be used to prove triangle congruence because it only shows that the triangles are similar, not necessarily congruent.

Front

What is the relationship between congruent triangles and their corresponding parts?

Back

If two triangles are congruent, then their corresponding sides and angles are also congruent.

Front

What is the definition of congruent triangles?

Back

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