Question

in triangle ABC ,D and E are mid points of the sides bc and AC respectively . find the length of DE . prove that DE =1/2 ab

Answer 1

Answer:

First Find the points D and E by midpoint formula.

(x₂+x₁/2 , y₂+y₁/2)

For DE=1/2AB

In ΔsCED and CAB

∠ECD=∠ACB

and the ratio of the side containing the angle is same i.e,

CD=1/2BC

⇒CD/BC=1/2

EC=1/2AC

⇒EC/AC=1/2

∴,ΔCED~ΔCAB

hence the ratio of their corresponding sides will be equal,

DE=1/2AB