Question

In the given below figure, in ∆ABC, D and E are the midpoint of the sides BC and AC respectively. Find the length of DE. Prove that DE = 1 /2 AB

Answer 1

hola there given:
ABC is a triangle , D and E are the 

mid-points of the sides BC and AC respectively.

TPT: DE=1/2 AB

proof:

since D and E are the mid-points of the sides BC and AC respectively.

therefore CD=1/2 BC and EC=1/2 AC.

now in the triangle CED and triangle CAB,

∠ECD=∠ACB

and the ratio of the sides containing the angle is same. i.e.

$\frac{cd}{ab} = \frac{1}{2} \: and \: \frac{ec}{ac} = \frac{1}{2}$
therefore the triangle CED and CAB are similar triangle.

hence the ratio of their corresponding sides will be equal.

hence 

$\frac{de}{ab} = \frac{1}{2}$
i.e. DE=1/2 AB