Gujarat BoardEnglish MediumSTD 9MathsLines And Angles3 Marks
Question
In figure, show that $AB\ ||\ EF$.
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Answer
Produce $EF$ to intersect $AC$ at $K$.
Now, $\angle\text{DCE}+\angle\text{CEF}=35+145=180^\circ$
Therefore, $EF\ ||\ CD ... (1)$ [Since Sum of Co-interior angles is $180$]
Now, $\angle\text{BAC}=\angle\text{ACD}=57^\circ$ $\Rightarrow BA\ ||\ EF ... (2)$ [Alternative angles are equal]
From $(1)$ and $(2)$ $AB\ ||\ EF$ [Since, Lines parallel to the same line are parallel to each other] Hence proved.
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