What is a Congruent Shape?

Congruent shapes have the same sides and angles. Any two similar shapes can be congruent, but if either the sides or the angles are different, they are not congruent. Understanding congruent shapes can help determine when shapes are the same even if they’re not drawn in the same orientation.

Congruent Circles

The main measurements of a circle are the circumference and the diameter or radius. If the diameter or radius of one circle is the same as another circle, they are congruent. Likewise, if the circumference for two circles is the same, the circles are congruent.

Congruent Polygons

Polygons have both sides and angles that need to be the same for the shapes to be congruent. For a square, knowing the size of one side on each can be helpful in determining if the squares are congruent as all 4 sides are going to be the same and all 4 angles are going to be 90 degrees. If the known sides are different between two squares, they are not congruent. With polygons that have more sides, it’s necessary to solve for all of the sides and angles for both shapes to determine if they’re congruent or now.

Determining if Two Shapes Are Congruent

To determine if two polygons are congruent, find the length of all of the sides and all of the angles. If all of them are the same, the two polygons are congruent. If anything is different, they are not going to be congruent. For example, one rectangle has 2 sides that are 4 inches and 2 sides that are 8 inches. All of the angles are 90 degrees. If another rectangle has 2 sides that are 4 inches and 2 sides that are 8 inches as well, the rectangles are congruent.

If a rectangle has 2 sides that are 5 inches and two sides that are 3 inches, and another one has 2 sides that are 4 inches and 2 sides that are 7 inches, these rectangles are not congruent. Even though they both have the same angles, they do not have the same side lengths and therefore are not the same.

Orientation Doesn’t Matter

When determining whether two polygons are the same, the orientation of them doesn’t matter. Picture a rectangle with horizontal sides 6 inches long and vertical sides 2 inches long. Then, picture another one that has horizontal sides 2 inches long and vertical sides 6 inches long. It appears as if the first rectangle is turned on its side to create the second one. Even though they look different, as long as the sides and angles have the same measurements, the two rectangles are congruent.

What is a congruent shape? If the sides and angles are the same on two shapes, the shapes are said to be congruent. Solving the sides and angles for one shape will mean the sides and angles for both shapes are solved. This can be useful for comparing two shapes and for determining how they are the same and if anything is different between them.