Question

Which of the following is a false statement?
(a) A median of a triangle divides it into two triangles of equal areas.
(b) The diagonals of a || gm divide it into four triangles of equal areas.
(c) In a ∆ABC, if E is the midpoint of median AD, then $\mathrm{ar}(∆BED)=\frac{1}{4}\mathrm{ar}(∆ABC)$.

(d) In a trap. ABCD, it is given that AB || DC and the diagonals AC and BD intersect at O. Then, ar(∆AOB) = ar(∆COD).

Answer 1

(d) In a trap. ABCD, it is given that AB || DC and the diagonals AC and BD intersect at O. Then ar(∆AOB) = ar(∆COD).


Consider ∆ADB and ∆ADC, which do not lie on the same base but lie between same parallel lines.
i.e., ar(∆ADB)$\ne$ ar(∆ADC)
Subtracting ar(∆AOD) from both sides, we get:
ar(∆ADB) $-$ ar(∆AOD) $\ne$ ar(∆ADC) $-$ ar(∆AOD)
Or ar(∆ AOB)$\ne$ ar(∆ COD)