Question

In the fig., ABC ad DCX are equilateral triangles, where D is the mid-point of BC. 4

If AX cuts BC at Y, prove that :

(i) ABY ~XCY

(ii) 3XC = AB

(iii) BY = 2YC​

Answer 1

Answer:

Answer

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=21AC........(1)

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

EF=21AB.........(2)

And we know, BE=21AB and BF=21BC.........(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.