
The diagonals of a rhombus bisect each other at ________angles.
A. Acute
B. Obtuse
C. Right
D. None
Answer
516.3k+ views
Hint: In this question is given that we have to find at what angles the diagonals of a rhombus bisects each other, so to find the solution first of all we need to draw a rhombus ABCD where AC and BD are the diagonals which interests each other at E.
For a rhombus AE=EC and BE=ED.
Complete step-by-step answer:
We know that the diagonals of a parallelogram bisect each other.
Also we know that every rhombus is a parallelogram, but the main difference is every side of a rhombus is equal, i.e, AB=BC=CD=DA.
Now for , we have,
CD=CB [Sides of a rhombus]
BE=ED [ since, diagonals bisects each other]
CE=CE [ common side]
So by SSS congruence (side-side-side) property, we can say that,
i.e,
As we know that ‘CPCT rule: if two or more triangles are congruent, then all of their corresponding angles and sides are congruent’
So by CPCT we can say that,
………..equation (1)
Since are linear pairs so the summation of the angles is .
i.e,
[by using equation(1)]
Now by equation (1) we can write,
Hence, the diagonals of a rhombus bisect each other at right angles.
So the correct option id option C.
Note: So to solve this type of problem you need to know that a rhombus is also a parallelogram but for a rhombus the corresponding sides are equal to each other, and also diagonals of a rhombus perpendicularly bisects each other.

For a rhombus AE=EC and BE=ED.
Complete step-by-step answer:
We know that the diagonals of a parallelogram bisect each other.
Also we know that every rhombus is a parallelogram, but the main difference is every side of a rhombus is equal, i.e, AB=BC=CD=DA.
Now for
CD=CB [Sides of a rhombus]
BE=ED [ since, diagonals bisects each other]
CE=CE [ common side]
So by SSS congruence (side-side-side) property, we can say that,
i.e,
As we know that ‘CPCT rule: if two or more triangles are congruent, then all of their corresponding angles and sides are congruent’
So by CPCT we can say that,
Since
i.e,
Now by equation (1) we can write,
Hence, the diagonals of a rhombus bisect each other at right angles.
So the correct option id option C.
Note: So to solve this type of problem you need to know that a rhombus is also a parallelogram but for a rhombus the corresponding sides are equal to each other, and also diagonals of a rhombus perpendicularly bisects each other.
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