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`

In the given figure two sides AB and BC and median AM of one triangle ABC are respectively equal to side PQ and QR and median PN of DeltaPQR . Show the DeltaABC~=DeltaPQR .

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see figure) Show that AD = AE

A line cuts two sides AB and side AC of DeltaABC in point P and Q respectively. Show that (A(DeltaABC))/((A(DeltaAPQ)))=(APxxAQ)/(ABxxAC)

If the median AD of triangle ABC makes an angle pi/4 with the side BC, then find the value of |cotB-cotC|dot

In the given Figure AB and CD are intersecting at ‘O’, OA = OB and OD = OC. Show that (i) Delta AOD ~= DeltaBOC and (ii) AD || BC .

In the adjoining figure "seg "Cebot" side " AB, " seg" AD bot" side " BC. Prove that (i) DeltaAEP~DeltaCDP (ii) DeltaAEP~DeltaADB

Let the incircle of a Delta ABC touches sides BC, CA and AB at D,E and F, respectively. Let area of Delta ABC be Delta and thatof DEF be Delta' . If a, b and c are side of Dela ABC , then the value of abc(a+b+c)(Delta')/(Delta^(3)) is

ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of DeltaPQR is double the perimeter of DeltaABC.

In a triangle ABC, if D and E are mid points of sides AB and AC respectively. Show that vecBE+ vecDC=(3)/(2)vecBC .