Gujarat BoardEnglish MediumSTD 8MATHSUnderstanding Quadrilaterals2 Marks
Question
Explain, how this figure is a trapezium? Which of its two sides are parallel?
✓
Answer
In the given figure, $\angle L=80^{\circ}, \angle M=100^{\circ}$ and $\angle L+\angle M=80^{\circ}+100^{\circ}=180^{\circ}$ We know that when a transversal cuts two lines such that pair of interior angles on the same side of the transversal are supplementary, then lines have to be parallel. Here, transversal $L M$ cut two lines $N M$ and $K L$ and pair of interior $\angle L$ and $\angle M$ are supplementary, so $N M \| K L$. Hence, it is a trapezium. $\quad[\because$ other two sides are not parallel$]$
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