Ex.3.3 Q10 Understanding Quadrilaterals Solution-Ncert Maths Class 8

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Question

 Explain how this figure is a trapezium. Which of its two sides are parallel? 

Text Solution

What is Known?

Given figure is a Quadrilateral.

What is Unknown?

To identify the two parallel sides of the figure and to prove that it is a trapezium.

Reasoning:

Trapezium is a quadrilateral having one pair of parallel sides.

Steps:

In the given figure \( KLMN\),

\(\angle {\rm{L }}\) + \({\rm{ }}\angle {\rm{M }}\) \(= {\rm{18}}0^\circ \) [two pair of adjacent angles (which form pairs of consecutive interior angles) are supplementary]

\[ = {\rm{ 8}}0^\circ {\rm{ }} + {\rm{1}}00^\circ = {\rm{18}}0^\circ \]

Therefore, \(KN\) is parallel to \(ML\)

Hence, \(KLMN\) is a trapezium as it has a pair of parallel sides: \(KN \) and \(ML\).