Chapter 5.4, Problem 15PSB

Solution

To Prove: The diagonals of a rectangle are congruent

Given information:

ABCD is a rectangle.

Concept used:

Here, we are using the concept of Side Angle Side property.

Proof:

  

Here, ABCD is a rectangle and also a parallelogram.

So, $AB\cong DC$ (Opposite sides are congruent)

And, In $\Delta ABC$ and $\Delta DCB$

  $BC=BC$ (Common)

  $\angle ABC=\angle DCB$ (Right angles)

  $AB=DC$ (Proved above)

So, $\Delta ABC\cong \Delta DCB$ (by using Side Angle Side property)

So, $AC\cong BD$ (by corresponding parts of congruent triangles) Hence proved