S and T are points on sides PR and QR of `trianglePQR` such that `angleP`=`angleRTS` .Show that `triangleRPQ~triangleRTS` .

In fig. D and E are points on side BC of triangleABC such that BD=CE and AD=AE. Show that triangleABDequivtriangleACE

In fig., (QR)/(QS)=(QT)/(PR) and angle1=angle2 . Show that trianglePQS~triangleTQR . .

D is a point on the side BC of a triangle ABC such that angleADC = angleBAC . Show that CA^2 = CB. CD.

Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of trianglePQR (see Fig.). Show that triangleABC ~ trianglePQR . .

Q is a point on the side SR of a trianglePSR such that PQ=PR. Prove that PS>PQ.

Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR are median PN of trianglePQR . Show that triangleABCequivtrianglePQR

Sides AB and AC and median AD of a triangle ABC are proportional to sides PQ and PR and median PM of another triangle PQR. Prove that triangleABC - trianglePQR . .

D is any point on side AC of triangleABC with AB=AC show that CD>BD.

D and E are points on sides AB and AC respectively of a DeltaABC such that ar (DeltaBCE) = ar (DeltaBCD) . Show that DE || BC .