If the angle of a quadrilateral are equal, how do you prove that it is a rectangle?

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Answer 1 · 2018-07-05T23:19:30

There needs to be either one right angle or the diagonals have to be congruent.

Let's say you have quadrilateral ABCD. If the opposite angles are congruent, then it is automatically a parallelogram as well.

According to the properties of a rectangle, it needs to have either one right angle or congruent diagonals.

#"To prove that ABCD has one right angle:"#

Prove that two sides are perpendicular. To find this, you can use the slope formula (#Deltay##/Deltax#), also known as (#y_2-y_1##/x_2-x_1#).

#" To prove diagonals are congruent:"#

Do the distance formula of the two diagonals. If they come out to be the same answer, then they are congruent.

#root##(x_2−x_1)^2+(y_2−y_1)^2# (Everything is under the radical here)