Congruence (geometry) facts for kids

The two triangles on the left are congruent. This means they are the same shape and size. The third triangle is similar, meaning it has the same shape but a different size. The last triangle is different from all the others.

In geometry, two shapes or objects are congruent if they are exactly the same. This means they have the same shape and the same size. Imagine you have two identical cookies. They are congruent! Even if you turn one cookie upside down or move it to a different spot, it's still the same cookie.

Sometimes, one shape might be the mirror image of the other. If you can flip one shape over and it matches the other perfectly, they are also congruent.

To be more exact, two shapes are congruent if you can move one of them so it fits perfectly on top of the other. You can slide it, turn it, or flip it over. But you cannot make it bigger or smaller. These movements are called rigid motions or isometry.

Think of it like this: If you draw two shapes on a piece of paper, they are congruent if you can cut them out and then make them match up perfectly. You are even allowed to turn one of the cut-out shapes over.

What Makes Shapes Congruent?

When shapes are congruent, it means all their matching parts are also congruent. For example, if two triangles are congruent, then:

• All their matching sides have the same length.
• All their matching angles have the same measure.

This is true for any type of shape, not just triangles. If you have two congruent squares, all their sides are equal, and all their angles are 90 degrees.

Congruent Polygons

A polygon is a closed shape made of straight lines, like a triangle or a square. Two polygons are congruent if they have the same number of sides, and all their matching sides and angles are equal.

For example, if you have two triangles, Triangle A and Triangle B:

• If side 1 of Triangle A is the same length as side 1 of Triangle B, and so on for all sides.
• And if angle 1 of Triangle A is the same measure as angle 1 of Triangle B, and so on for all angles.

Then, Triangle A and Triangle B are congruent!

Images for kids

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  The orange and green shapes are congruent. They are the same shape and size. The blue shape is not congruent to them, even though it has the same perimeter and area.

See also

In Spanish: Congruencia (geometría) para niños