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,

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