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

$\sf ✵Given✵$

• : 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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