Triangle congruence

Front

What is the definition of triangle congruence?

Back

Triangle congruence means that two triangles are congruent if they have the same size and shape, which can be proven using various congruence theorems.

Front

What does the SSS congruence theorem state?

Back

The SSS (Side-Side-Side) congruence theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What does the SAS congruence theorem state?

Back

The SAS (Side-Angle-Side) congruence theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What does the ASA congruence theorem state?

Back

The ASA (Angle-Side-Angle) congruence theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What does the AAS congruence theorem state?

Back

The AAS (Angle-Angle-Side) congruence theorem states that 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 two triangles are congruent.

Front

What is the definition of corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are the angles and sides that are in the same relative position in each triangle.

Front

How can you prove that two triangles are congruent using the SSS theorem?

Back

To prove that two triangles are congruent using the SSS theorem, you must show that all three pairs of corresponding sides are equal in length.

Front

How can you prove that two triangles are congruent using the SAS theorem?

Back

To prove that two triangles are congruent using the SAS theorem, you must show that two pairs of corresponding sides are equal in length and the angle between those sides is also equal.

Front

What is the significance of the congruency statement ΔBAC≅ΔBAD?

Back

The congruency statement ΔBAC≅ΔBAD indicates that triangle BAC is congruent to triangle BAD, meaning all corresponding sides and angles are equal.

Front

What is the relationship between congruence and similarity in triangles?

Back

Congruence means that triangles are identical in size and shape, while similarity means that triangles have the same shape but may differ in size.