Question

the given figure, ray PQ || ray RS, ray PN is the bisector of ∠QPR and ray RM is the bisector of ∠PRS. Prove that line PM || line RM. Q N R P M S Given: Ray PQ || ray RS, and ray PN and ray RM are the bisectors of ∠QPR and ∠PRS respectively. To prove: line PN || line RM Solution: Proof: Ray PQ || ray RS and seg PR is their transversal. ∴ ∠QPR = ∠PRS ….(i) [ ……………… ] ∠NPR = ½ ∠ ……… [Ray PN bisects ∠QPR] ∴ 2∠NPR = ∠QPR …..(ii) [……….]= ½ ∠PRS [Ray RM bisects ∠PRS] ∴ 2∠MRP = […………] …(iii) ∴ 2∠NPR = 2∠MRP [From (i), (ii) and (iii)] ∴ ∠NPR = ………… But, ∠NPR and ∠MRP are alternate angles on lines PN and RM when seg PR is the transversal. ∴ line PN || line RM [ ….…….. ]


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Answer 1

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