Question

in triangle abc,Dand E are midpoints of the sides BC and ACrespectively find the length of DE prove that DE=1/2AB

Answer 1

Answer:

Step-by-step explanation:

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

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