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

1 Answer
Jul 5, 2018

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

Explanation:

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)