Question

(a) In the given figure, if PQ $∥$ RS, then prove that $△ POQ \sim △ SOR$ .

(b) In the given figure, $△ OSR \sim △ OQP$ , $∠ ROQ = 125°$ and $∠ ORS = 70°$ . Find the measures of $∠ OSR$ and $∠ OQP$ .

Approach

Given PQ parallel to RS, prove triangle POQ is similar to triangle SOR. Since PQ ∥ RS, corresponding angles are equal: $∠ P = ∠ S$ and $∠ Q = ∠ R$ (alternate interior angles). By AA similarity criterion, $△ POQ \sim △ SOR$ .

Step-by-step working

1
As $PQ ∥ RS$ , $∠ P = ∠ S$ (alternate interior angles)
1 mark
2
$∠ Q = ∠ R$ (alternate interior angles)
3
$∴ △ POQ \sim △ SOR$ (by AA similarity criterion)
1 mark

Concepts used

similar trianglesproveparallel linescorresponding anglesaa similarityfind angle

Approach

Step-by-step working

Concepts used

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