Mathematics
Two parallelogram ABCD and ABEF are equal in area, they lie between the same parallel lines:
Yes
No
Nothing can be said
Theorems on Area
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Answer
While it is a known geometric theorem that parallelograms on the same base and between the same parallels are equal in area, the converse is not strictly true in the way this question is phrased.
In above case both parallelograms share the base AB. However, simply having the same area and the same base does not automatically mean they must lie between the same parallels unless it is specified that they are on the same side of the base.
Thus, nothing can be said.
Hence, option 3 is the correct option.
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Related Questions
The area of given parallelogram is:
AB x BM
BC x BN
DC x DL
AD x DL
ABCD is a quadrilateral whose diagonals intersect each other at point O. The diagonal AC bisects diagonal BD. Then area of quadrilateral ABCD is :
2 x area of ΔABD
2 x area of ΔBCD
4 x area of ΔAOB
2 x area of ΔABC
ABCD is a trapezium with parallel sides AB = a cm and DC = b cm. E and F are the mid-points of the non-parallel sides. The ratio of ar.(ABFE) and ar.(EFCD) is:
a : b
(3a + b) : (a + 3b)
(a + 3b) : (3a + b)
(2a + b) : (3a + b)
Statement 1: ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area.
Statement 2: It is not necessary that the quadrilateral ABCD is a rectangle or a parallelogram or rhombus.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.