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.