Question

Example 5 : If a transversal intersects two lines such that the bisectors of a pair of
corresponding angles are parallel, then prove that the two lines are parallel.
step by step explanation.​

Answer 1

Answer:

given: A transversal AB intersects two lines PQ and RS such that < PLM = 2 SML

To prove: PQ || RS

Proof: PLM = < SML (given).

(i)

SML = RMB . (ii) (vertically opposite

angles)

From equations (i) and (ii),

< PLM = RMB

As these are corresponding angles and corresponding angles equal only if given lines PQ and RS are parallel.

:: PQ || RS

Step-by-step explanation:

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