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

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## Question

Given a parallelogram $$ABCD$$. Complete each statement along with the definition or property used.

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

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

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

(iv) $$m\,\angle DAB\, + \,m\,\angle CDA\, =\_\_\_\_\_\_\_$$ ## Text Solution

What is Known?

$$ABCD$$ is a parallelogram.

What is Unknown?

$${\rm{AD}},\,\,\angle DCB,\,\,\,{\rm{OC}},\,\,{\rm{m}}\angle DAB + {\rm{m}}\angle CDA$$

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,

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

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