Triangle Congruence

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a rule 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 ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a rule 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 does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a rule 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 SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a rule that states if two sides and the included angle of one triangle are congruent to two sides and the corresponding included angle of another triangle, then the triangles are congruent.

Front

Can triangles be congruent if they are only similar?

Back

No, triangles that are only similar (AAA) are not necessarily congruent. Similar triangles have the same shape but may differ in size.

Front

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

Back

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

Front

What is a congruence statement?

Back

A congruence statement is a way to express that two triangles are congruent, indicating the corresponding vertices of the triangles, such as △ABC ≅ △PQR.

Front

How do you determine if two triangles are congruent using AAS?

Back

To determine if two triangles are congruent using AAS, check if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle.

Front

What is the difference between congruent and similar triangles?

Back

Congruent triangles are identical in shape and size, while similar triangles have the same shape but may differ in size.

Front

What is the purpose of using congruence rules in geometry?

Back

Congruence rules help to determine whether two triangles are the same size and shape, which is essential for solving various geometric problems.