Congruent Circles

In geometry, congruency is the term used to refer objects that have the same shape and size (dimension). Like all other geometric figures such as triangles, quadrilaterals or a polygon, two circles can also be congruent.

What are Congruent Circles

A circle is defined by two properties: its center and its radius. Since congruency is independent of position and a circle remains the same regardless of rotation and reflection, the circle’s congruence depends only on its radius.

Again, since a radius ‘r’ is a constant (that does not change its value) and it is only equal to another constant, then all circles with the same radii (or any value dependent on radii) are congruent to each other.

Also, we know that when the radii of two circles are equal, their diameter (twice the circle’s radius), area, and perimeter are also equal.

Thus, congruent circles are defined as circles that have the same radius, diameter, area, and perimeter. When two circles have the same radius, diameter, surface area, and perimeter, they will be of the same shape or dimension. Thus, congruent circles can also be defined as circles that have the same shape or dimension such that they can overlap.

Shown below are two congruent circles.

Are All Circles Congruent

As we know, two circles are congruent only when they have the same shape and size. Since all circles are of the same shape but their size can vary based on their radius, all circles are similar but not congruent.