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In the below fig, show that AB || EF.

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#### Solution

Produce *E**F *to intersect AC at K.

Now, `∠`*DCE *+ `∠`*CEF *= 35° +145° = 180°

*∴EF *|| *CD *[ ∵ Sum of Co-interior angles is 180°] ……(1)

Now, `∠`*BAC *= `∠`*ACD *= 57°

*⇒ BA *|| *CD [∵ *Alternative angles are equa*l] ……(2)*

From (1) and (2)

*AB *|| *EF *[Lines parallel to the same line are parallel to each other]

Hence proved.

Concept: Lines Parallel to the Same Line

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