In triangle ABC D abd E are midpoint of side BC and AC respectively. Find length of DE . Prove that DE =1/2 AB?

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In triangle ABC D abd E are midpoint of side BC and AC respectively. Find length of DE . Prove that DE =1/2 AB?

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In triangle ABC D abd E are midpoint of side BC and AC respectively. F...

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 the 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

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