Question

In the given figure, PR is a line segment, a line
segment PQ is parallel to the another line
segment RS and O is the mid-point of QS. Then
prove that
(I) 2op = pr​

Answer 1

Given: AB is parallel to another line segment CD.  

           O is the midpoint OF AD

In ΔAOB and ΔDOC

∠AOB=∠COD         ...(Vertically opposite angle )

∠BAO=∠CDO         ...(Given AB parallel to DC and AD meet  both lines so alternate angles are equal)

AO=OD          ....(O is the midpoint of AD )

ΔAOB≅ΔDOC        ...ASA test

So, BO=CO

Then, O is the midpoint of BC.

Answer 2

to prove : 2op = Pr

answer : consider triangle POQ and SOR

• SO = OQ (given that o is mid point of qs )
• angle PQO = angle OSR (alternate angles)
• angle POQ = angle SOR (verticaly opposite angles )

HENCE : triangles POQ and triangle SOE are equal

[sides opposite to equal angles are equal ]

OP = OR

PO and OR are equal they are same in length

• HENCE : 2OP = PR