diagonals of the rectangle are drawn from opposite vertices.
one diagonal is top left to bottom righgt.
the other diagonal is bottom left to top right.
these diagonals form 2 right triangle.
the top right triangle has the 90 degree angle at the top left of the rectangle.
the bottom right triangle has the 90 degree angle at the bottom right of the rectangle.
these right triangles are congruent to each other by SAS.
since they are congruent to each other, then their corresponding sides are all congruent.
this includes the diagonals of the rectangle which means that the diagonals of the rectangle are also congruent.
if you use coordinate geometry to prove that they are congruent, all you have to do is find the length of the top of the rectangle and the length of the bottom of the rectangle and then solve for the length of the diagonals by using the pythagorean formula.
the following picture shows the rectangle and the triangles formed by the diagonals and the geometric interpretation of the proof that the diagonals are congruent to each other.
the following picture shows the rectangle on a graph with coordinate points at each corner and how you would calculate to prove that the diagonals are congruent to each other.
basically you use the coordinate points to find the length and the width of the triangle and then you use the pythagorean formula to find the length of the diagonals.
since the legs of each of the right triangles formed are congruent to each other, and the triangles formed are congruent to each other, then the formula for the diagonals will be identical and the result will be to show that the diagonals are congruent to each other because they have the same length and shape (their shape is a straight line)