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Theorem 6.4 : If a transversal intersect...

Theorem 6.4 : If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.

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Since ray `ND` stands on line `EF`,
`/_3 + /_5=180 ` (linear pair of angles)
But, `/_ 1 = /_5` (Corresponding angles as `AB∣∣CD`)
From above equations, we get `/_ 1+ /_ 3=180`
Again ray `CN` stands on `EF`,
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Theorem 6.5 : If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.

Knowledge Check

  • If a transversal line cuts two parallel lines then bisector of internal angle formed a

    A
    rectangle
    B
    square
    C
    rhombus
    D
    parallelogram

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