Triangle Congruence

Front

What does it mean for triangles to be congruent?

Back

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

Front

What is the SAS (Side-Angle-Side) Congruence Postulate?

Back

If two sides of one triangle are equal to two sides of another triangle, and the angle between those sides is equal, then the triangles are congruent.

Front

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

Back

If two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the triangles are congruent.

Front

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

Back

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

Front

What is the SSS (Side-Side-Side) Congruence Postulate?

Back

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

Front

What is the SSA (Side-Side-Angle) condition?

Back

SSA does not guarantee triangle congruence; it can lead to ambiguous cases where two different triangles can be formed.

Front

How do you denote triangle congruence?

Back

Triangle congruence is denoted using the symbol '≅'. For example, ∆ABC ≅ ∆XYZ means triangle ABC is congruent to triangle XYZ.

Front

What is the importance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which helps in proving congruence and solving problems.

Front

What is a congruence statement?

Back

A congruence statement lists the triangles that are congruent and matches their corresponding parts. For example, ∆ABC ≅ ∆DEF.

Front

Can two triangles be congruent if only one angle is known?

Back

No, knowing only one angle is not sufficient to prove congruence; additional information about sides or other angles is needed.