Question

In the given figure O is the midpoint of PQ , PS || RQ . Prove that ∆POS =~ ∆ ROQ and hence prove that SO = OR.​

Answer 1

in triangle pos and triangle roq

po=oq (divided equally)

angle pos=angle roq(vertically opposite angles)

so=or

by sas, criteria

pos congruent to roq

Answer 2

Given : O is the midpoint of PQ, PS||RQ  

To Find :  prove that ∆POS =~∆ROQ and hence prove that SO = OR​

Solution:

in Δ POS  & Δ QOR

∠SPO = ∠RQO   ( alternate interior angles as PS || RQ  & PQ is transversal)

PO  =  OQ    As O is mid point

∠POS = ∠OQR  ( vertically opposite angles)

=> Δ POS  ≅  Δ QOR   ASA

Corresponding sides of Congruent triangles are Equal

=>    OS = OR

=> SO = OR

QED

Hence Proved

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