Problem
GEO-B1-M04-P003 Diagonals of a Rectangle
#3
★☆☆☆☆ Level 1 of 5
Prove that the diagonals of a rectangle are equal.
Compare two right triangles with a common side.
Let \(ABCD\) be a rectangle. Consider triangles \(ABC\) and \(DCB\). We have \(AB=CD\) because a rectangle is a parallelogram, side \(BC\) is common, and angles \(ABC\) and \(DCB\) are right. Thus the triangles are congruent, so \(AC=BD\).
It is important that the student proves the equality of diagonals, not just recalls it.