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, by alternate interior angles, $∠ P = ∠ S$ and $∠ Q = ∠ R$ . Therefore, by AA similarity criterion, $△ POQ \sim △ SOR$ .

Step-by-step working

1
Since $PQ ∥ RS$ , $∠ P = ∠ S$ and $∠ Q = ∠ R$ (alternate interior angles).
1 mark
2
By AA similarity criterion, $△ POQ \sim △ SOR$ .
1 mark

Concepts used

similar trianglesprove similaritycorresponding anglesfind angle

Approach

Step-by-step working

Concepts used

Similar question types