## Definition: having the same shape and size Example: 2 rectangles have to be the same

### Definition: In mathematics, objects are said to be “congruent” when they have the same size and shape

Definition: In mathematics, objects are said to be “congruent” when they have the same size and shape. This means that if two objects are congruent, all corresponding sides and angles of the objects are equal. Congruent objects can include shapes such as triangles, quadrilaterals, circles, or three-dimensional objects like cubes or spheres.

For example, let’s consider two rectangles. In order for them to be congruent, they must have the same length and width. This means that if one rectangle has a length of 5 units and a width of 3 units, the other rectangle must also have a length of 5 units and a width of 3 units.

It is important to note that congruence refers to the relationship between two objects. If two objects are congruent, we can say that one is the same size and shape as the other. However, congruence does not imply that the two objects are in the same location or orientation in space.

When working with congruent shapes, we can use this property to prove various geometric theorems and relationships. For instance, if we prove that two triangles are congruent, we can then infer that their corresponding angles and sides are equal, allowing us to establish other properties or solve geometric problems.

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