Question

d e f are mid points of sides bc ca ab of ∆abc find the ratio of areas of ∆def and ∆abc​

Answer 1

Answer:

1:4

Step-by-step explanation:

since d, e and f are mid points of the sides

so by midpoint theorem,

de||ab, ef||bc, df||ac

and the lines are half on the sides.

so, angle DFB = angle BAC

df||ac, the angles are corresponding.

similarly, angle FDB=angle ACB

so, DFB ~ ACB

similarly, we obtain that all the smaller triangles are similar to ABC

by these, we can say all smaller triangles are congurent. so, they will have the same area

so indirectly, the triangle is divided in four equal parts bg area.

so, ar( DEF ): ar( ABC) =1:4