Question

adjoining figure triangle ABC is an equilateral triangle. K e and e are midpoints of side a b side bc and ac respectively prove that triangle kej it is also an equilateral triangle​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given: ∆ABC is an equilateral triangle.  Points F, D and E are midpoints of side AB, side BC, side AC respectively.  To prove: ∆FED is an equilateral triangle.  Proof:  ∆ABC is an equilateral triangle. [Given]  ∴ AB = BC = AC ….(i) [Sides of an equilateral triangle]  Points F, D and E are midpoints of side AB and BC respectively. ∴ FD = (1/2)AC …..(ii) [Midpoint theorem]  Points D and E are the midpoints of sides BC and AC respectively.  ∴ DE = (1/2)AB …..(iii) [Midpoint theorem]  Points F and E are the midpoints of sides AB and AC respectively.  ∴ FE = (1/2) BC  ∴ FD = DE = FE [From (i), (ii), (iii) and (iv) ]  ∴ ∆FED is an equilateral triangle.