Prove that the diagonals of the rectangle are equal.

Let AВСD be a rectangle. In a rectangle, sides AB and СD are parallel, and BC and AD are also parallel. Consider the triangles AВD and ABC. These are right-angled triangles, <A = <B = 90 °. In triangles ABD and ABC, side AB is common, and sides BC = AD, as opposite sides in a parallelogram or rectangle.

But in equal triangles opposite to equal sides there are equal sides, which means that the sides against equal right angles <A = <B = 90 °, the sides ВD and AC are equal. And these are the diagonals of the rectangle. Proven. …