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ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD
a. is a rectangle
b. is always a rhombus
c. is a parallelogram
d. need not be any of (A), (B) or (C)

Solution:

ABCD need not be a rectangle, parallelogram and rhombus

If ABCD is a square, the diagonal AC divides it into two parts of equal area

Therefore, ABCD need not be any of (A), (B) or (C).

✦ Try This: The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 7 cm and 5 cm is :

It is given that

Length of rectangle = 7 cm

Breadth of rectangle = 5 cm

Consider E, F, G and H as the mid-points of sides AB, BC, CD and AD

EFGH is a rhombus

Diagonals are EG and HF

So EF = BC = 7 cm

HF = AB = 5 cm

We know that

Area of rhombus = Product of diagonals/ 2

By further calculation

= (7 × 5)/2

= 35/2

= 17.5 cm²

Therefore, the figure obtained is a rhombus of area 17.5 cm².

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 9

NCERT Exemplar Class 9 Maths Exercise 9.1 Problem 8

ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD a. is a rectangle, b. is always a rhombus, c. is a parallelogram, d. need not be any of (A), (B) or (C)

Summary:

ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD need not be any of (A), (B) or (C)

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