The base BC of `Delta ABC` is divided at D, so that `BD=1/2DC`.Prove that `ar(Delta ABD)`=`1/3ar(Delta ABC)`

The base BC of triangle ABC is divided at D so that BD = (1)/(2) DC. Prove that area of DeltaABD=(1)/(3) of the area of DeltaABC .

Delta ABC and Delta BDC are on the same base BC. Prove that (ar(Delta ABC))/(ar(Delta DBC)) =(AO)/(DO)

ABCD is a trapezium in which AB I I DC. DC is produced to E such tha t CE= AB, prove that ar( Delta ABD) = ar( Delta BCE).

In the given figure, Delta ABC and Delta DBC have the same base BC. If AD and BC intersect at O, prove that (ar(DeltaABC))/(ar(Delta DBC))=(AO)/(DO)

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar( Delta AOD) = ar( Delta BOC).

In Delta ABC,AD and BE are altitudes.Prove that (ar(Delta DEC))/(ar(Delta ABC))=(DC^(2))/(AC^(2))

In the same figure, Delta ABC and Delta DBC are on the same base BC . If AD is intersects BC at O, prove that (ar(Delta ABC))/(ar (Delta DBC))=(AO)/(DO)

In figure , D and E are Points on side BC of a Delta ABC such that BD = CE and AD = AE . Show that Delta ABD cong Delta ACE.

ABCD is a trapezium with AB||DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar( Delta ADX) = ar( Delta ACY).

In figure ,D and E are Points on side BC of a Delta ABC such that BD=CE and AD=AE.Show that Delta ABD cong Delta ACE.