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Q.

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


(a) ABCD is square


(b) diagonal BD bisects Question Image as well as Question Image


Which of the following statements is correct?


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a

 a

b

 b

c

 a and b

d

 None of these

answer is C.

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Detailed Solution

Concept: Make the diagram of rectangle using the conditions diagonal AC bisects Question Image as well as Question Image. To prove the further points, apply the properties of triangles.
Given that,
In rectangle ABCD, AC bisects Question Image as well as Question ImageQuestion ImageIt implies that,
Question ImageQuestion ImageNow, from the figure Question Image.
Also, Question Image is transversal of the parallel lines
Therefore, Alternate interior angles will be equal Question ImageOr Question Image from equation (1)
As we know that, Sides opposite to the equal angles are equal i.e., Question ImageAnd Opposite sides of the rectangle are equal So, Question ImageFrom equation (4) and (5)
Question ImageABCD 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.
Question Image BD bisects Question Image as well as Question ImageHence, 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?