# Ex.3.3 Q1 Understanding Quadrilaterals Solution-Ncert Maths Class 8

## Question

Given a parallelogram \(ABCD\). Complete each statement along with the definition or property used.

(i)\(\, AD\, = \,\_\_\_\_\_\_\_\_\_\)

(ii)\(\, \angle DCB\, = \,\_\_\_\_\_\_\)

(iii)\(\,OC\, = \,\_\_\_\_\_\_\_\_\)

(iv) \(\,m\,\angle DAB\,\!\!+\!\!\,m\,\angle CDA\,\!\!=\_\_\_\_\_\_\_\)

## Text Solution

**What is Known?**

\(ABCD\) is a parallelogram.

**What is Unknown?**

\(\begin{align}&{\rm{AD}},\angle DCB,\,{\rm{OC}},\,\,\\&{\rm{m}}\angle DAB +\!{\rm{m}}\angle CDA\end{align}\)

**Reasoning:**

We can use the properties of parallelogram to determine the solution.

**Steps:**

i) The opposite sides of a parallelogram are of equal length.

\({\rm{AD }} = {\rm{ BC}}\)

(ii) In a parallelogram, opposite angles are equal in measure.

\(\angle {\rm{DCB }} = {\rm{ }}\angle {\rm{DAB}}\)

(iii) In a parallelogram, diagonals bisect each other. Hence,

\({\rm{OC }} = {\rm{ OA}}\)

(iv)In a parallelogram, adjacent angles are supplementary to each other. Hence,

\(m\angle {\rm{DAB }} + {\rm{ m}}\angle {\rm{CDA }} = {\rm{18}}0^\circ \)