Medians QT and RS of `Triangle PQR` intersect at X. Show that `ar(triangle XQR)` is equal to `ar (quad SXTP)`

Medians QT and RS of Tri anglePQR intersect at X.Show that ar(/_XQR) is equal to ar(SXTP)

If the medians of a triangle ABC intersect at G, show that ar(triangleAGB)=ar(triangleAGC)=ar(triangleBGC) =(1)/(3)ar(triangleABC) .

Diagonal PR and QS of quadrilateral PQRS intersects at T such that PT= TR and PS= QR, show that ar (Delta PTS) =" ar "(Delta RTQ)

If the medians of a triangleABC intersect at G, show that ar(AGB) = ar(AGC) = ar(BGC) = 1/3 ar(ABC)

If the medians of a triangleABC intersect at G, show that ar(AGB) = ar(AGC) = ar(BGC) = 1/3 ar(ABC)

If PS is median of the triangle PQR, then ar( Delta PQS): ar( Delta QRP) is

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar( Delta AOD) = ar( Delta BOC). Prove that ABCD is a trapezium.

E is any point on median AD of a triangle ABC . Show that ar (ABE) = ar (ACE).

In a triangle ABC, E is the mid-point of median AD. Show that ar (triangleBED)=1/4 ar( triangleABC ).