In the triangle ABC,D and E are the midpoints of the sides BC and AC respectively.Find the length of DE.Prove that DE=1/2AB.

 

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.

therefore the triangle CED and CAB are similar triangle.

hence the ratio of their corresponding sides will be equal.

hence  i.e. DE=1/2 AB

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