Chapter 5.4, Problem 14PSB

Solution

To Prove: Each pair of opposite sides in a parallelogram are congruent.

Given information:

ABCDis a parallelogram.

Concept used:

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

Proof:

  

Here, $AB\parallel CD$ and $AD\parallel BC$ (because ABCD is a parallelogram)

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

  $\angle 1=\angle 4$ (Alternate interior angles)

  $AC=AC$ (Common)

  $\angle 2=\angle 3$ (Alternate interior angles)

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

So, $AB\cong DC$ and $AD\cong BC$ (by corresponding parts of congruent triangles) Hence proved