Question

ABCD is a quadrilateral in which AD = BC. E, F, G and H are mid-points of AB, BD, CD and AC respectively. Then EFGH is a -

• A. Square
• B. Rectangle
• C. Kite
• D. Rhombus

Answer 1

The correct option is D

Rhombus

Using mid-point theorem,

In $\Delta DBC,GF=\frac{1}{2}BC$

In $\Delta ACD,GH=\frac{1}{2}AD$

In $\Delta ABC,EH=\frac{1}{2}BC$

In $\Delta BAD,EF=\frac{1}{2}AD$

Since AD = BC,

we can say that GF = GH = EH = EF

$\Rightarrow$ EFGH is a rhombus.