Question

ABC is a quadrilateral and its diagonals AC and BD intersect in O prove that if BO =OD, the triangle ABC and ADC are equal in area

Answer 1

Given

ABCD is a parallelogram

AC and BD are diagonals

O is a mid point

To prove BO =OD

O=o common point

Angle b=angle d opp angles in ll gm are                     equal

Ob=od sides opp to equal angles are equal

Hence proved

Answer 2

Given: area of triangle ABC = area of triangle ADC.

Solution: ar. triangle ABC = 1/2×AC ×

AB (equation 1st).

ar.triangle ADC= 1/2×AC×OD (equation 2nd)

compare equation first and second :

1/2×AC×OB = 1/2 × AC ×OD

OB = OD.

proved.