Congruent Triangles

A construction team is building the roof of a house. They begin by placing roof trusses. Each truss has triangular sections that support the roof.

The team first designs one triangular section. Then, they need to make more triangles of the same size and shape. In geometry, triangles with the same size and shape are called congruent triangles.

Congruent triangles have corresponding sides of equal length and corresponding angles of equal measure. A triangle can slide, flip, or turn and still be congruent because its size and shape stay the same.

We do not need to check every side and angle to know whether two triangles are congruent. Instead, we use triangle congruence criteria. Let’s go over some of them.

In SSS, or Side-Side-Side, all three corresponding sides of two triangles are equal in length.

In SAS, or Side-Angle-Side, two corresponding sides and the included angle are equal in measure.

In ASA, or Angle-Side-Angle, two corresponding angles and the included side are equal in measure.

These criteria help confirm that triangular sections have the same size and shape. This helps keep the roof even and properly shaped.