Three statements are given below: (i) In a rectangle ABCD, the di… - Vidyadip

MCQ

Three statements are given below:
$ (i)$ In a rectangle $\text{ABCD},$ the diagonal $AC$ bisects $\angle\text{A}$ as well as $\angle\text{C}.$
$(ii)$ In a square $\text{ABCD},$ the diagonal $AC$ bisects $\angle\text{A}$ as well as $\angle\text{C}.$
$(iii)$ In a rhombus $\text{ABCD},$ the diagonal $AC$ bisects $\angle\text{A}$ as well as $\angle\text{C}.$ Which is true?

A
$I$ only
✓
$II$ and $III$
C
$I$ and $III$
D
$I$ and $II$

✓

Answer

Correct option: B.

$II$ and $III$

Consider $I$.
We know that, in a rectangle the diagonals are not bisectors of each other, since the adjacent side.
Thus, $I$ is false.
Consider $II$.
We know that, in a square the diagonals bisect the opposite angles.
So, in a square $\text{ABCD},$ the diagonals $AC$ bisects $\angle\text{A}$ as well as $\angle\text{C}.$
Thus, $II$ is true.
Consider $III$.
We know that, in a rhombus the diagonals bisect the opposite angles.
So, in a rhombus $\text{ABCD},$ the diagonals $AC$ bisects $\angle\text{A}$ as well as $\angle\text{C}.$
Thus, $III$ is true.

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