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`.

If a straight line intersects the sides AB and AC of a triangle ABC at D and E respectively and is parallel to BC , then (AE)/(AC) = . ………..

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

If D is the midpoint of the side BC of a triangle ABC, prove that vec(AB)+vec(AC)=2vec(AD)

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.

Show that the median of a triangle divides it into two triangles of equal areas.

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

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)

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