Question

Prove that the diagonals of a rectangle bisect each other. the midpoint of is _____

Answer 1

In this attached picture, we can prove that triangles AOB and COD are congruent. ∠CDO and ∠ABO are equal because they are alternate angles. Similarly, ∠OAB and ∠OCD are equal because they are alternate angles, as well. We have a rectangle and in the rectangle, opposite sides are equal; AB = CD. Then, because of Angle-SIde-Angle principle, we can say that triangles AOB and COD are equal. If triangles are congruent, then OD = OB and OC = AO. Applying congruency to the triangles ACD and BCD, we can see that these triangles are also congruent. It means that the diagonals are equal. Since, OD = OB and OC = AO, it proves that the point O simultaneously is the midpoint and intersection point for the diagonals.