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Theorem 6.5 : If a transversal intersect...

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.

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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 6.4 : 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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Knowledge Check

  • If two lines are intersected by a transversal, then the number of pairs of interior angles on the same side of the transversal is

    A
    1
    B
    2
    C
    3
    D
    4

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    Theorem 6.3 : If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.

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    Fill in the blanks in each of the following to make the statement true: (i) If two parallel lines are intersected by a transversal, then each pair of corresponding angles are.... (ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are... (iii) Two lines perpendicular to the same line are.... to each other. (iv) Two lines parallel to the same line are .......... to each other. (v) If a transversal intersects a pair of lines in such away that a pair of alternate angles are equal, then the line are... (vi) If a transversal intersects a pair of lines in such away that the sum of interior angles on the same side of transversal is 180,then the line are .......

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