Congruent shapes

From Graphic maths
Level: GCSE Maths

Two shapes are congruent if they are the same size and the same shape. These three shapes are congruent:

Congruent-poly.png

Shapes A and B are congruent because they are the same size and shape. It doesn't matter that shape B is rotated.

Shape C is also congruent with A and B. It is reflected, but it is still congruent.

Congruent polygons

Two polygons are congruent if all their corresponding sides and angles are equal.

Having equal sides is not enough to guarantee that two shapes are congruent. For example this square and rhombus both have four equal sides, but they have different angles, so they are not the same shape:

Incongruent-poly-angles.png

Having equal angles is not enough to guarantee that two shapes are congruent. For example this square and rectangle both have four right angles, but they have different length sides, so they are not the same shape:

Incongruent-poly-sides.png

Equal sides and angles are required.

Triangles

For congruent triangles there are special rules.

Other shapes

Other shapes can be congruent. For example, two circles with the same radius are congruent.

See also