# Basic geometry proof

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• September 5th 2011, 07:10 AM
MichaelLight
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
• September 5th 2011, 07:35 AM
Plato
Re: Basic geometry proof
Quote:

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.