8
Question
In the figure given below, state which lines are parallel and why?
In the figure given below, state which lines are parallel and why?
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Solution
ANSWER:
Here, ∠BAC = ∠ACD = 110°
Thus, lines AB aand CD are intersected by a transversal AC such that the pair of alternate angles are equal.
∴ AB || CD (If a transversal intersects two lines such that a pair of alternate interior angles are equal, then the
two lines are parallel)
Thus, line AB is parallel to line CD.
Also, ∠ACD + ∠CDE = 110° + 80° = 190° ≠ 180°
If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal are
supplementary, then the two lines are parallel.
Therefore, line AC is not parallel to line DE.
Here, ∠BAC = ∠ACD = 110°
Thus, lines AB aand CD are intersected by a transversal AC such that the pair of alternate angles are equal.
∴ AB || CD (If a transversal intersects two lines such that a pair of alternate interior angles are equal, then the
two lines are parallel)
Thus, line AB is parallel to line CD.
Also, ∠ACD + ∠CDE = 110° + 80° = 190° ≠ 180°
If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal are
supplementary, then the two lines are parallel.
Therefore, line AC is not parallel to line DE.
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