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

2 = 3, 1 ≠ 4

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1 = 2 = 3 = 4

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1 ≠ 2, 3 = 4

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1 = 2, 3 ≠ 4

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Solution

The correct option is B 1 = 2 = 3 = 4
Consider the figure below:

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

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

If 1, 2, 3 and 4 represent the areas of the four triangles of a parallelogram with different shades, then $1 = 2$ ≠ $3 = 4$

Q. If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the area of the parallelogram is
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 3 : 4
Figure

In a triangle and a parallelogram are on the same base and between the same parallels then the ratio of the area of the triangle to the area of the parallelogram is

(a) 1:2

(b) 1:3

(d) 3:4

Q. Question 9
If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of the parallelogram is:

A) 1:3
B) 1:2
C) 3:1
D) 1:4

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