MCQ
The two diagonals are equal in a:
- ✓Rectangle
- BRhombus
- CParallelogram
- DTrapezium
✓
Answer
Correct option: A.
Rectangle
$ABCD$ is a rectangle with $AC$ and $BD$ as its diagonals.
$ABCD$ is a rectangle
$\therefore \angle\text{A} = 90^\circ, \ \text{AD = BC}$
$\text{AD || BC}$ and AB is a transversal
$\therefore \angle\text{A} + \angle\text{B} = 180^\circ$
$\Rightarrow \angle\text{B} = 90^\circ$
In $\triangle\text{ABD}$ and $\triangle\text{BAC}$
$AB = BA$
$\angle\text{A} = \angle\text{B}$
$AD = BC$
$\therefore \triangle\text{ABD}≅\triangle\text{BAC} (SAS)$
$\Rightarrow BD = AC (c.p.c.t)$
Hence, the diagonals of a rectangle are equal.
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