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ABCD is a rectangle in which diagonal AC bisects as well as .Then,

(a) ABCD is square

(b) diagonal BD bisects as well as

Which of the following statements is correct?

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a and b

None of these

answer is C.

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Detailed Solution

Concept: Make the diagram of rectangle using the conditions diagonal AC bisects

as well as

. To prove the further points, apply the properties of triangles.
Given that,
In rectangle ABCD, AC bisects

as well as

It implies that,

Now, from the figure

.
Also,

is transversal of the parallel lines
Therefore, Alternate interior angles will be equal

from equation (1)
As we know that, Sides opposite to the equal angles are equal i.e.,

And Opposite sides of the rectangle are equal So,

From equation (4) and (5)

ABCD is a square (all sides of the square are equal).
Now, it is the property of the square that both the diagonals of the square bisects the angle into two equal parts.

BD bisects

as well as

Hence, the correct answer is option (3).

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ABCD is a rectangle in which diagonal AC bisects as well as .Then,(a) ABCD is square(b) diagonal BD bisects as well as Which of the following statements is correct?

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ABCD is a rectangle in which diagonal AC bisects as well as .Then,

(a) ABCD is square

(b) diagonal BD bisects as well as

Which of the following statements is correct?