Question

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

Answer 1

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.