# In triangle PQR point T is the mid point of median PS as shown in the given fig show that ar(triangle PQT)=1/4 ar(triangle PQR)

To prove : ar (triangle PQT) = 1/4 ar(triangle PQR)

construction: join TR

ar(triangle PQS) = ar(triangle PSR)

therefore, half of Ar(triangle PQS) = half of Ar ( triangle PSR)

that is Ar(triangle PQT)=Ar(triangle PTR)...........(1)

and Ar(triangle QST) = Ar( triangle TSR)...........(2)

since, Ar (triangle PQR) =ar (triangles PQS + PSR )

but from (1) and (2)

ar (triangle PQR) = 2ar(trianlge PQS)

ar (triangle PQR) =2ar(2PQT)....from (1)

ar (triangle PQR) = 4 ar (triangle PQT )

therefore,ar(triangle PQT) = 1/4 ar (triangle PQR)

hope this helps if so, dont forget to make that thumbs up button go dark blue!!