Topic Consolidation: Congruency and Similarity

CONGRUENCY

A pair of triangles are considered to be congruent if they fulfil any of the following criteria:

SSS (Side-Side-Side)

Each side of the first triangle must be the same length as the corresponding side of the second triangle.

SAS (Side-Angle-Side)

Two pairs of sides of the first triangle must be equal to another pair of sides on the second, the angle that they enclose must also be the same.

AAS (Angle-Angle-Side)

Two angles and one side must be the same.

RHS (Right Angle-Hypotenuse-Side)

The triangles must have a right angle (angle that is 90 degrees) and their hypotenuse and a side must be equal.

SIMLARITY

Triangles are said to be similar if they fulfil any of the following criteria:
SSS (Side-Side-Side)

Each side of the first triangle must be the same length as the corresponding side of the second triangle.

SAS (Side-Angle-Side)

Two pairs of sides of the first triangle must be equal to another pair of sides on the second, the angle that they enclose must also be the same.

AA (Angle-Angle)

Two angles in both triangles must be the same.

APPLICATION

If two triangles are congruent, their sides will equal each other.

If two triangles are similar, SIDE A of triangle 1 over SIDE A of triangle 2 will be equal to SIDE B of triangle 1 over SIDE B of triangle 2.

Side A and Side B being the corresponding sides.