The two diagonals are equal in a: - Vidyadip

MCQ

The two diagonals are equal in a:

A
Rectangle
B
Rhombus
C
Parallelogram
D
Trapezium

✓

Answer

Rectangle
Solution:

ABCD is a rectangle with AC and BD as its diagonals.
ABCD is a rectangle
$∴ \angle\text{A} = 90^\circ, \ \text{AD = BC}$
$\text{AD || BC}$ and AB is a transversal
$∴ \angle\text{A} + \angle\text{B} = 180^\circ$
$⇒ \angle\text{B} = 90^\circ$
In $\triangle\text{ABD}$ and $\triangle\text{BAC}$
AB = BA
$\angle\text{A} = \angle\text{B}$
AD = BC
$∴ \triangle\text{ABD}≅\triangle\text{BAC}$ (SAS)
⇒ BD = AC (c.p.c.t)
Hence, the diagonals of a rectangle are equal.

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