Question

Prove the mid point theorem analytically

Answer 1

The line segment joining the midpoints of two sides of a triangle is parallel to the third side and also half of it.

Answer 2

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This answer is verified ✅✅


In ∆AED and CEF ,

AE = CE (given)
/_DAE = /_FCE [ Alternate Interior Angles]
/_AED = /_CEF ( vert.oppo.angles)
∆AED =~∆ CEF

AD = CF and DE = EF (c.p.c.t)

But, AD = BD
BD = CF and BD||CF. (netting DE produced in F)
BCFD is a ||gm.

DF|| BC and DF = BC
DE||BC and DE = 1/2DF = 1/2 BC [ DE = EF]

Hence DE ||BC and DE = 1/2BC..

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