Altitudes and Medians

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• Oct 21st 2011, 09:31 PM
blahblahblah1234
Altitudes and Medians
Hi guys,

So I had a question about altitudes and medians. If two altitudes of a triangle are congruent to each other, then the medians of the corresponding sides are also congruent. Is this statement always true or is there an exception?

Thanks - blahblahblah1234
• Oct 22nd 2011, 06:12 AM
skeeter
Re: Altitudes and Medians
Quote:

Originally Posted by blahblahblah1234
Hi guys,

So I had a question about altitudes and medians. If two altitudes of a triangle are congruent to each other, then the medians of the corresponding sides are also congruent. Is this statement always true or is there an exception?

Thanks - blahblahblah1234

note that the area of a triangle is $A = \frac{1}{2}bh$

if $h$ is an altitude, then $b$ is the side perpendicular to that altitude

so ...

$\frac{1}{2} b_1 h_1 = \frac{1}{2} b_2 h_2$

if $h_1 = h_2$ , what does that say about the lengths of the two corresponding sides, $b_1$ and $b_2$ ?

further ... what kind of triangle would this be, and what can you say about the lengths of the medians to these two corresponding sides?
• Oct 22nd 2011, 10:01 AM
blahblahblah1234
Re: Altitudes and Medians
Thanks skeeter, haha. Soo the triange would be isoceles or equilateral and the medians would be congruent to the altitudes. Thanks again.