Rectangle. Rectangle Tag

A rectangle is called a parallelogram, in which all angles are right angles.



Theorem.

If a parallelogram has all angles equal, then it is a rectangle.

Evidence.

Let a parallelogram ABCD be given and ∠ A = ∠ B = ∠ С = ∠ D.

Angles A and B are internal one-sided, which means their sum is 180 º. By the condition they are equal, it means that each of them is equal to 90 º. Therefore, ∠ A = ∠ B = ∠ С = ∠ D = 90 º. A parallelogram with all angles right is a rectangle. The theorem is proved.