# Math Help - Basic geometry proof

1. ## Basic geometry proof

Given a triangle ABC and D is the midpoint of BC. Prove that

(a) AD < (AB+AC)/2

(b) AD > (AB+AC-BC)/2

2. ## Re: Basic geometry proof

Originally Posted by MichaelLight
Given a triangle ABC and D is the midpoint of BC. Prove that
(a) AD < (AB+AC)/2
(b) AD > (AB+AC-BC)/2
Using vectors this is rather easy.
$\overrightarrow {DA} = \overrightarrow {AB} + \overrightarrow {BD} \;\& \,\overrightarrow {DA} = \overrightarrow {AC} + \overrightarrow {CD}$
Note that $\overrightarrow {BD}+\overrightarrow {CD}=0$.

Use the triangle inequality.