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Question Number 17692 by b.e.h.i.8.3.417@gmail.com last updated on 09/Jul/17

Answered by Tinkutara last updated on 09/Jul/17

Commented by b.e.h.i.8.3.417@gmail.com last updated on 09/Jul/17

thanks sir.nice and smart.

$${thanks}\:{sir}.{nice}\:{and}\:{smart}. \\ $$

Commented by Tinkutara last updated on 09/Jul/17

E and F are the midpoints of sides AB and AC. ∴ EF ∥ BC and EF = ((BC)/2). ...(i) Similarly M and N are the midpoints of sides DE and DF. ∴ MN ∥ EF and MN = ((EF)/2). ...(ii) From (i) and (ii), we get MN ∥ BC and MN = ((BC)/4).

$${E}\:\mathrm{and}\:{F}\:\mathrm{are}\:\mathrm{the}\:\mathrm{midpoints}\:\mathrm{of}\:\mathrm{sides} \\ $$$${AB}\:\mathrm{and}\:{AC}. \\ $$$$\therefore\:{EF}\:\parallel\:{BC}\:\mathrm{and}\:{EF}\:=\:\frac{{BC}}{\mathrm{2}}.\:...\left({i}\right) \\ $$$$\mathrm{Similarly}\:{M}\:\mathrm{and}\:{N}\:\mathrm{are}\:\mathrm{the}\:\mathrm{midpoints}\:\mathrm{of} \\ $$$$\mathrm{sides}\:{DE}\:\mathrm{and}\:{DF}. \\ $$$$\therefore\:{MN}\:\parallel\:{EF}\:\mathrm{and}\:{MN}\:=\:\frac{{EF}}{\mathrm{2}}.\:...\left({ii}\right) \\ $$$$\mathrm{From}\:\left({i}\right)\:\mathrm{and}\:\left({ii}\right),\:\mathrm{we}\:\mathrm{get} \\ $$$${MN}\:\parallel\:{BC}\:\mathrm{and}\:{MN}\:=\:\frac{{BC}}{\mathrm{4}}. \\ $$

Commented by alex041103 last updated on 09/Jul/17

Beautiful!

$$\mathrm{Beautiful}! \\ $$

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