Question

Which of the following is a false statement ?

(a) A median of a triangle divides it into two triangles of equal area.

(b) The diagonals of a ||gm divide it into four triangles of equal area.

(c) In a $△ABC$,if E is the midpoint of median AD then ar($△ABC$)=$\frac{1}{4}ar\left(△ABC\right)$.

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

Answer 1

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