prove that each angle of a rectangle is a right angle ?

Consider the following figure of rectangle.

The diagonals AC and BD intersect at O.

Thus the vertical angles

Since the line segments AB and CD are parallel lines, and AC is the transversal, then the alternate interior angles

Since the line segments AB and CD are parallel lines, and BD is the transversal, then the alternate interior angles

The sides AD = BC

Therefore, by Angle-Side-Angle congruence,

AB and CD are parallel, and BD is a transversal, therefore, the angles.

Now,

and

Thus,

We also know that in a parallelogram, the sum of opposite angles are 180 degrees.

Also

Since , they have to be equal to 90 degrees each.

Thus, in a rectangle all the angles are 90 degrees.

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