Question

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

(a) square

(b) rectangle

(c) parallelogram

(d) rhombus

Answer 1

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 = \(\frac 12\)AC   ......(1)

Since, F is mid point of BC and E is mid point of AC, by mid point theorem,

EF = \(\frac 12\)AB   .......(2)

And we know,

BE = \(\frac 12\)AB and BF = \(\frac 12\)​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.