Mathematics
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.
Theorems on Area
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Answer
Let ABCD be a quadrilateral such that each diagonal divides it into triangles of equal areas, then
Area of △ABC = Area of ABCD, ……………….(1)
Area of △ADC = Area of ABCD, ……………….(2)
From (1) and (2) we get,
Area of △ABC = Area of △ADC.
So, statement 1 is true.
The condition that a diagonal divides a quadrilateral into two parts of equal area does not restrict the quadrilateral to be a rectangle, parallelogram, or rhombus.
∴ Statement 2 is true.
∴ Both the statements are true.
Hence, option 1 is the correct option.
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Related Questions
Two parallelogram ABCD and ABEF are equal in area, they lie between the same parallel lines:
Yes
No
Nothing can be said
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)
Assertion (A): PQRS a parallelogram whose area is 180 cm2 and A is any point on the diagonal PR. The area of triangle ASR = 30 cm2.
Reason (R): A is not the mid-point of diagonal PR.
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.
Assertion (A): ABCD is a square. E is mid-point of side AB and F is mid-point of side DC. If DA = 16 cm, the area of triangle COF is 32 cm2.
Reason (R): EF is ⊥ to DC and OF = DA = 8 cm.
Area of COF = x CF x OF
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.