Examples on Parallelogram

Example 1: If EC = 7, Find BC.

Solution:

A diagonal of a parallelogram are bisecting each other. Thus, BE≅ EC or BE = EC.

Therefore, BC = 2 (EC)

BC = 2 (7)

BC = 14

Example 2: Two adjacent sides of a parallelogram are AC = 5 cm and CD = 2 cm. Find its perimeter.

Solution:

In parallelogram opposite sides are always equal.

As we have a parallelogram ABCD;

In this, AC = BD = 5 cm

CD = AB = 2 cm,

Perimeter of Parallelogram = 2 ( AC + CD) = 2(5 + 2) cm

= 2 ( 7) cm

= 14 cm

Example 3: If m ∠ ABC = 65 and m ∠BAC = 55, Find m∠ DBC.

Solution:

In parallelogram, Consecutive angles are supplementary

So, we have m∠BAC + m∠ABC = 180°

But, m∠ABD = m∠ABC + m∠DBC

m∠ABD = 65 + m∠DBC

Therefore, m∠DBC = 180 – (m∠BAC + m∠ABC)

m∠DBC = 180 – (55 + 65)

m∠DBC = 180 -120

m∠DBC = 60

Parallelograms are fundamental geometric shapes in mathematics that are basically used in various fields like architecture, Engineering, and others. They can even be found in common places near you like windows, doors, tables, etc. where their symmetrical characteristics enhance both functionality and beauty.

Understanding the various applications of parallelograms enhances our awareness of the value of geometry in everyday situations.