Question

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

Answer 1

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)