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Provide solution for RD Sharma maths class 12 chapter Scaler and Dot Product exercise 23.2 question 2

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Answer: Yes, quadrant bisects  at 90^{0} each other

Hint: Use rhombus

Given: Prove that if diagonal of quadrant bisects each other at right angle

Then it is rhombus.

Solution: Take quadrilateral ABCD , ACand BD are diagonals which intersect at 0

In \; \triangle \; A O B \; and \; \triangle A O D\\\\ \begin{array}{ll} D O=O B & \text { (O is midpoint) } \\ A O=A O & \text { (common side) } \end{array}

\angle A O B=\angle A O D \quad\left(90^{\circ}\right. Right \; angle ) \\\\So, \triangle A O B \cong \triangle A O D\\\\ So, A B=A D

Similarly, AB=BC=CD=AD


can proved which mean that ABCD is rhombus
 

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