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 = 1/2AB

Answer 1

First Find the points D and E by midpoint formula.(x₂+x₁/2 , y₂+y₁/2)For DE=1/2ABIn ΔsCED and CAB∠ECD=∠ACBand the ratio of the side containing the angle is same i.e,CD=1/2BC⇒CD/BC=1/2EC=1/2AC⇒EC/AC=1/2∴,ΔCED~ΔCABhence the ratio of their corresponding sides will be equal,DE=1/2AB
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