Question

Am is a median of a triangle ABC is a b + BC + CA is equal to 2 a.m.

Answer 1

Step-by-step explanation:

Yes! AB + BC + CA > 2 AM

AM is a median. So, BM = CM

CONSTRUCTION: Extend AM to D, such that AM= MD

=> ABDC is a parallelogram ( as diagonals are bisecting each other)

Since, AB + BM > AM……………..(1) ( The sum of 2 sides of a triangle > third side)

& BD + BM > MD ………….(2) ( the same reason)

Now, by adding (1) & (2)

We get, AB + BD + 2 BM > AM + MD ………(3)

But BD = AC ( opposite sides of parallelogram)

& 2BM = BC

& AM = MD

SO, Eq (3) becomes

AB + AC + BC = 2AM

[ proved]

Answer 2

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

In triangle ABM

AB+BM = AM............. →(1)

In triangle ACM

AC+CM = AM............. →(2)

adding equation (1) and (2)

AB+AC+(BM+CM) = 2AM

⇒AB+AC+BC = 2AM