Parallelograms Theorem 4

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Recall that the diagonals of a parallelogram bisect each other. Since a rectangle is also a parallelogram, the diagonals of a rectangle also bisect each other.

What is the additional property of the diagonals of a rectangle?

Let us draw a rectangle and measure its diagonals.

By measurement, you will find that

diagonal AC=diagonal BD

Let us prove this logically.

Statement

The diagonals of a rectangle are equal in length.

Given:

ABCD is a rectangle.

AC and BD are diagonals.

To prove:

AC=BD

Proof:

Now in triangles, ABD and ABC,

AB=AB (common side)

(each angle is a right angle)

AD=BC (opposite sides of parallelogram)

BD=AC (corresponding parts of

corresponding triangles)

Hence the theorem is proved.