Proving Similar Triangles

AA similarity (Angle-Angle) means that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

SAS similarity (Side-Angle-Side) means that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

SSS similarity (Side-Side-Side) means that if the three sides of one triangle are in proportion to the three sides of another triangle, then the triangles are similar.

You can determine if two triangles are similar by using the AA, SAS, or SSS similarity postulates.

The triangles are similar by the AA similarity postulate.

The triangles are similar by the SAS similarity postulate.

The triangles are similar by the SSS similarity postulate.

The included angle is the angle between the two sides being compared; it must be equal for the triangles to be similar.

No, if two triangles have no equal angles, they cannot be similar.

If triangle ABC has angles of 30°, 60°, and 90°, and triangle DEF has angles of 30°, 60°, and 90°, then they are similar by AA similarity.