In the given figure, ABC and DBC are two triangles on the same base BC. Prove that `(ar(ABC))/(ar(DBC))= (AO)/(DO)`.

In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that (ar(ABC))/(ar(DBC))= (AO)/(DO) .

In the figure, ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by bar(AB) at O, show that ar (DeltaABC) = ar (DeltaABD).

In the given figure, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that : (CA)/(PA)=(BC)/(MP)

ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that angle ABD = angle ACD .

In the given figure, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that : DeltaABC ~ DeltaAMP

triangle ABC and triangle DBC are isosceles triangles on the same base BC. Prove that line AD bisects BC at right angles

ABC and ADC are two right triangles with common hypotenuse AC. Prove that angle CAD = angle CBD.

In the given figure, ABC is a triangle right angled at B. D and E are ponts on BC trisect it. Prove that 8AE^(2) = 3AC^(2) + 5AD^(2) .

In triangle ABC, AD is a median. Prove that AB + AC gt 2AD

triangle ABC and triangle DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that, ( i ) triangle ABD = triangle ACD (ii) triangle ABP = triangle ACP (iii) AP bisects angle A as well as angle D. (iv) AP is the perpendicular bisector of BC