Question

AD is a median of triangle ABC Show that AB +BC+AC>2AD​

Answer 1

Answer:

Proved that from triangle ABC where AD is median, AB + BC + CA > 2AD. We will be using the property of triangle which says SUM OF TWO SIDES OF TRAINGLE IS ALWAYS GRATER THAN THIRD SIDE

Answer 2

given,

ad is the median of Δabc

to prove,

ab + ac > 2ad

construction,

produce ad to E such that ad = de and join ce

ad = de(Construction)

∠adb = ∠cde(Vertically opposite angles)

bd = dc(ad is the median from A to BC)

∴ Δabd congruent to  Δcde by (SAS rule)  

⇒ ab = ce(cpct) ...(1)

In Δace

ac + ce > AE(Sum of any two sides of a triangle is greater than the third side)

⇒ ac + ab > ad + de [Using (1)]

⇒ ac + AB > ad + ad(Constriction)

⇒ ac + ab > 2ad {proved}