Question

Given an equilateral triangle ABC, D, E, and F are the mid-points of the sides AB, BC, and AC, respectively, then the quadrilateral BEFD is exactly a

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

Answer 1

The correct option is D rhombus

Given, ABC is an equilateral triangle.D, E, F are mid points of the sides of the triangle.
Since, D is mid point of AB and E is mid point of AC, by mid point theorem,
$DE=\frac{1}{2}AC$........(1)
Since, F is mid point of BC and E is mid point of AC, by mid point theorem,
$EF=\frac{1}{2}AB$.........(2)
And we know, $BE=\frac{1}{2}AB$ and $BF=\frac{1}{2}BC$.........(3)
Now, from (1), (2) and (3)
Since, all the sides of equilateral triangle are equal,
$DE=EF=BE=BF$
Hence, BEFD is a rhombus.