Question

If ∠1 = ∠3 and ∠2 = ∠4 and AB = BC, then the given quadrilateral is a ____________ .

• A. parallelogram
• B. rhombus
• C. trapezium
• D. rectangle

Answer 1

The correct option is B rhombus

From the given figure,
ABCD is a quadrilateral and AC is one of its diagonal.

Given,
∠1 = ∠3 and ∠2 = ∠4
Also, AB = BC
$\Rightarrow$∠1 = ∠4 (Isosceles triangle)

So, in $△ABC\text{and}△ADB$
∠1 = ∠3,
Side CA is common,
and ∠2 = ∠4
$\therefore △ABC\cong △ADB$

$\Rightarrow$ AB = BC = AD = DC (by cpct)
So, the quadrilateral ABCD is a rhombus.