Question

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.

Options

• 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.

Answer 1

Both the statements are true.

Explanation:

• Statement (1): If a diagonal AC of a quadrilateral ABCD divides it into two triangles (ΔABC and ΔADC) with equal areas, then Statement (1) describes a valid condition for such a quadrilateral.
• Statement (2): A kite or a general quadrilateral can have a diagonal that splits it into two equal-area triangles without being a parallelogram, rectangle, or rhombus. Thus, it is not necessary for the quadrilateral to be a parallelogram, rectangle, or rhombus, making Statement (2) true as well.