D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that `AE^2+BD^2=AB^2+DE^2` .

ABC is an isosceles triangle right angled at C. Prove that AB^2 = 2AC^2 .

BL and CM are medians of a triangle ABC right angled at A. Prove that 4 ( BL^2 + CM^2 ) = 5 BC^2 .

D and E are points on sides AB and AC respectively of DeltaABC such that ar (DBC) = ar (EBC). Prove that DE II BC .

D,E and F are mid-points of the sides BC, CA and AB respectively of triangleABC . Prove that ar(||gmBDEF)= 1/2 ar (triangleABC)

If D, E and F are three points on the sides BC, CA and AB, respectively, of a triangle ABC such that the lines AD, BE and CF are concurrent, then show that " "(BD)/(CD)*(CE)/(AE)*(AF)/(BF)=1

In the fig D,E and F are the mid points of the sides BC,CA and AB respectively of triangleABC . If BE and DF intersect at X while CF and DE ntersect at Y. prove that XY=1/4BC

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

Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ || AB and QR || BC, prove that RP II CA.

ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segent AX bot DE meets BC at Y. Show that: ar(CYXE) = 2ar(FCB)

D,E,F are the middle points of the sides [BC],[CA],[AB] respectively of a triangle ABC. Show that : FE is parallel to BC and half of its length.