Q34 of 109 Page 318

Three statements are given below:

I. In a rectangle ABCD, the diagonal AC bisects ∠A as well as ∠C.


II. In a square ABCD, the diagonal AC bisects ∠A as well as ∠C.


III. In a rhombus ABCD, the diagonal AC bisects ∠A as well as ∠C.


Which is true?

We can clearly observe that statement II and statement III are correct and Statement I is wrong because the diagonals of a rectangle does not bisect ∠A and ∠C. And this is so because the adjacent sides are unequal in a rectangle.


∴ Option B is correct

More from this chapter

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32

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O such that ∠DAC = 30° and ∠AOB = 70°. Then, ∠DBC = ?

 33

Three statements are given below:

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


II. The angle bisectors of a ||gm 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 is true?

 35

In each of the questions one question is followed by two statements I and II. Choose the correct option.

Is quadrilateral ABCD a ||gm?


I. Diagonals AC and BD bisect each other.


II. Diagonals AC and BD are equal.

 36

In each of the questions one question is followed by two statements I and II. Choose the correct option.

Is quadrilateral ABCD a rhombus?


I. Quad. ABCD is a ||gm.


II. Diagonals AC and BD are perpendicular to each other.