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.
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