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

True

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False

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Solution

The correct option is B
False

Consider the figure below:

In $△ D A O$ and $△ O C B$
$∠ D A O = ∠ O C B (Alternate angles)$
$∠ A D O = ∠ C B O (Alternate angles)$
AD=CB \text{(Opposite sides of parallelogram)}
Hence, $Δ A D O ≅ Δ C B O (AAS congruence)$
Similarly it can be proved that
Area( $Δ$ DOC)=Area( $Δ$ (BOA) \)
therefore 1 = 3 and 2= 4.
Hence the given statement is false.

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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 _______.

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. 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

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

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