Question

in the triangle POQ and ROS, O is the midpoint prove that 2OP=PR​

Answer 1

given : PQ||RS

O is mid pt. of PS i.e. PO=OS

To prove : PQ=RS

Proof: In ∆POQ and ∆ROS

anglePOQ = angleROS (vertical opposite angles)

PO=OS (prooved above)

anglePQO =angle ORS (alternate interior angle)

By AAS congruence , ∆POQ congruent to ∆ORS

By cpct , PQ=RS