If 1, 2, 3 and 4 represent the areas of the four triangles (of a parallelogram)

Question

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

Options:

A . 2 = 3, 1 ≠ 4

B . 1 = 2 = 3 = 4

C . 1 ≠ 2, 3 = 4

D . 1 = 2, 3 ≠ 4

Answer: Option B
:
B
Consider the figure below:

△ D A O and △ O C B

∠ D A O = ∠ O C B (Alternate angles) ∠ A D O = ∠ C B O (Alternate angles) A D = C B (Opposite sides of parallelogram) Hence, Δ A D O ≅ Δ C B O (AAS congruence) Similarly it can be proved that A r e a (Δ D O C) = A r e a (Δ (B O A)

△ A B D

, AO is the median.
A median divides a triangle into two equal parts.
Hence 1 = 4
Similarly 2 = 3

∴ 1 = 2 = 3 = 4

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