Three statements are given below:

I. In a parallelogram, the angle bisectors of two adjacent angles enclose a right angle.

II. The angle bisectors of a parallelogram form a rectangle.

III. The triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle.

Which one is true?

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I only

II only

I and II

II and III

answer is C.

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Detailed Solution

Given 3 statements.
I. In a parallelogram, the angle bisectors of two adjacent angles enclose a right angle.
II. The angle bisectors of a parallelogram form a rectangle.
III. The triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle.
As, in a parallelogram the angle bisectors intersect and form a right-angle.
Hence, statement I is true.
The angle bisector forms a rectangle as it also intersects at the right-angle.
The statement II is also correct.
Hence, option 3 is correct.

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