Chapter 9.6, Problem 14PSB

To determine

To Prove: Diagonals of a rectangle are congruent.

Explanation of Solution

Given information:

ABCD is a rectangle.

Concept used:

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

Proof:

  

Since ABCD is a rectangle, it is also a parallelogram.

  $AB\cong DC$ (because opposite sides of a parallelogram are congruent)

  $BC\cong BC$ (by reflexive property of congruence)

  $\angle ABC\cong \angle DCB$ (since all right angles are congruent)

  $\therefore \Delta ABC\cong \Delta DCB$ (by Side Angle Side congruency)

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