Two sides AB, BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of `DeltaPQR` (See figure). Show that:
`(i) DeltaABM ~= DeltaPQN`
`(ii) DeltaABC ~= DeltaPQR`

Two sides AB, BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of trianglePQR (see figure). Show that: triangleABC~=trianglePQR

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure) . Show that (i) DeltaABD ~= DeltaACE (ii) AB = AC i.e., ABC is an isosceles triangle.

AB and CD are respectively the small est and longest sides of a quadrilateral ABCD (see figure). Show that angleAgtangleC and angleBgtangleD .

ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB espectively. Line segments AX bot DE meets BC at Y. and DE at X. Join AD, AE also BF and CM (See the figure). Show that (i) DeltaMBC ~=DeltaABD

AB and CD are respectively the smallest and longest sides of aquadrilateral ABCD (see adjacent figure). Show that /_A > /_C and /_ B > /_ D.

AB and CD are respectively the small est and longest sides of a quadrilateral ABCD (see adjacent figure).Show that /_Agt/_C /_Bgt/_D .

CM and RN are respectively the medians of similar triangle DeltaABC and DeltaPQR . Prove that DeltaAMC~DeltaPNR

If the mid points of the sides BC, CA and AB of a triangle ABC are respectively (2,1) (-01,-2)and (3,3) then the equation of the side BC is