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In the Below Fig, Show that Ab || Ef. - Mathematics

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

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Solution

Produce EF 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 equal]                      ……(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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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.4 | Q 21 | Page 48

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