Question

If ABC is a triangle and D is the midpoint of BC, then Ab+AC+2AD is equal to what? (ab ac and ad are vectors)

Answer 1

Answer:This is :-

Explanation:

This can be proved by making a small construction. Extend AD to E such that AD = DE. Join BE and CE. So, AE = 2AD ---------- (1)  

ii) In the quadrilateral, ABEC, the diagonal AE and BC bisect each other at D. [Since by construction AD = DE and as given AD is the median to BC; so D is the midpoint of BC]  

Since diagonals bisect each other, the quadrilateral ABEC is a parallelogram.  

In a parallelogram opposite sides are equal; so BE = AC --------- (2)  

iii) In triangle ABE, AB + BE > AE [Sum of any two sides of a triangle is greater than  

the third side]  

So from (1) & (2)  

AB + AC > 2AD

Answer 2

Answer:

Explanation:

This can be proved by making a small construction. Extend AD to E such that AD = DE. Join BE and CE. So, AE = 2AD ---------- (1)

ii) In the quadrilateral, ABEC, the diagonal AE and BC bisect each other at D. [Since by construction AD = DE and as given AD is the median to BC; so D is the midpoint of BC]

Since diagonals bisect each other, the quadrilateral ABEC is a parallelogram.

In a parallelogram opposite sides are equal; so BE = AC --------- (2)

iii) In triangle ABE, AB + BE > AE [Sum of any two sides of a triangle is greater than

the third side]

So from (1) & (2)

AB + AC > 2AD

Hope thse helps u