Question

If 1, 2, 3 and 4 represent the areas of the four triangles (of a parallelogram) with different shades, then _______.

• A. 2 = 3, 1 ≠ 4
• B. 1 = 2 = 3 = 4
• C. 1 ≠ 2, 3 = 4
• D. 1 = 2, 3 ≠ 4

Answer 1

The correct option is B 1 = 2 = 3 = 4

Consider the figure below:

In $△DAO\text{and}△OCB$
$\angle DAO=\angle OCB\text{(Alternate angles)}\angle ADO=\angle CBO\text{(Alternate angles)}AD=CB\text{(Opposite sides of parallelogram)}\text{Hence,}\Delta ADO\cong \Delta CBO\text{(AAS congruence)}\text{Similarly it can be proved that}Area\left(\Delta DOC\right)=Area\left(\Delta \right(BOA)$
In $△ABD$, AO is the median.
A median divides a triangle into two equal parts.
Hence 1 = 4
Similarly 2 = 3
$\therefore 1=2=3=4$​