The Rectangle Corollary: Identifying Rectangles by Congruent Opposite Sides

Rectangle Corollary

The Rectangle Corollary is a mathematical principle related to rectangles

The Rectangle Corollary is a mathematical principle related to rectangles. It states that if a quadrilateral has both pairs of opposite sides congruent, then it is a rectangle.

In order to understand the Rectangle Corollary, let’s first define a few terms. A quadrilateral is a polygon with four sides. Opposite sides of a quadrilateral are those that are not adjacent or next to each other. Congruent sides are sides that have the same length or measurement.

Now, according to the Rectangle Corollary, if a quadrilateral has both pairs of opposite sides congruent, it is a rectangle. This means that if you have a quadrilateral where the opposite sides have equal lengths, then you can conclude that it is a rectangle.

To further clarify this concept, let’s consider an example. Suppose we have a quadrilateral ABCD. If AB and CD are congruent, and AD and BC are also congruent, we can say that ABCD is a rectangle.

This is because, in a rectangle, opposite sides are parallel and congruent. So if all four sides of the quadrilateral are congruent, it implies that the quadrilateral has all the properties of a rectangle, such as right angles and congruent opposite sides.

It is important to note that the Rectangle Corollary is a useful tool when determining whether a given quadrilateral is a rectangle. However, it is not a proof by itself. To provide a rigorous proof, additional supporting evidence or theorems may be required.

In summary, the Rectangle Corollary states that if a quadrilateral has both pairs of opposite sides congruent, it is a rectangle. This principle helps in identifying rectangles based on the lengths of their sides, and it is commonly used in geometry to determine the shape of a given quadrilateral.

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