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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The transversal `AD` intersects the two lines `PQ` and `RS` at points `B` and `C` respectively. `BE` is the bisector of `/_ABQ` and `CF` is the bisector of `/_BCS`.
As, `BE` is the bisector of `/_ABQ`, then,
`/_ABE= 1/2 /_ABQ`
In the same way,
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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.
If a transversal intersects two parallel lines, then alternate interior angles are on the _______ side of the transversal.
If a transversal intersects two parallel lines; then each pair of consecutive interior angles are supplementary.
