Triangle Congruence

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

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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 two triangles are congruent.

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

ASA requires the included side to be congruent, while AAS does not require the side to be included between the two angles.

No, knowing only one angle is not sufficient to determine triangle congruence.

The included angle is the angle between the two sides being compared, which is crucial for establishing congruence.

If Triangle ABC has sides of lengths 5 cm, 7 cm, and 9 cm, and Triangle DEF has sides of lengths 5 cm, 7 cm, and 9 cm, then Triangle ABC is congruent to Triangle DEF by SSS.

If Triangle GHI has angles of 30° and 60° and the included side is 10 cm, and Triangle JKL has angles of 30° and 60° with the same included side of 10 cm, then Triangle GHI is congruent to Triangle JKL by ASA.