Question

in the following figure , l parallel to m and TR is a transversal. if OP and RS are respectively bisector of corresponding angles TOB and ORD, prove that OP|| RS

Answer 1

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Answer 2

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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