Tell whether the following statement is true or false:

In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O. If BO = OD, then area of triangle ABC = area of triangle ADC.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given a quadrilateral ABCD in which BO = OD.
In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O. If BO = OD, prove that ar (△ ABC) = ar (△ ADC). - Sarthaks eConnect | Largest Online Education Community

In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O. If BO = OD, prove that ar (△ ABC) = ar (△ ADC). - Sarthaks eConnect | Largest Online Education Community

Since AO is median on side BD.
Area of triangle AOB = Area of triangle AOD
Similarly, CO is median on side BD.
Area of triangle BOC = Area of triangle DOC
Combining both equations,
Area of triangle AOB + Area of triangle BOC = Area of triangle AOD + Area of triangle DOC
Area of triangle ABC = Area of triangle ADC
Given statement is true.
Hence, option 1 is correct.

Watch 3-min video & get full concept clarity