In the following figure | | m and TR is a transversal, if OP and RS are respectively bisector of corresponding ∠ TOB and ∠ORD, prove that OP ∥ RS.
Answers
The proof is given below:
∵ l ║ m and TR is a transversal line
∴ ∠TOB = ∠ ORD (corresponding angles)
Given that
OP is angle bisector of ∠TOB
∴ ∠TOP = ∠POB = (1/2)∠TOB
Similarly,
∠ORS = ∠SRD = (1/2)∠ORD
∵ ∠TOB = ∠ ORD (proved above)
∴ (1/2)∠TOB = (1/2)∠ ORD
or, ∠TOP = ∠ORS
If we consider OP and RS as two lines cut by a transversal line TR then ∠TOP and ∠ORS will constitute corresponding angles
We know that when such corresponding angles are equal, the lines are parallel
Therefore,
OP ∥ RS (Proved)
Hope this answer is helpful.
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