1. ## 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

2. ## Re: Altitudes and Medians

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 $\displaystyle A = \frac{1}{2}bh$

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

so ...

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

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

further ... what kind of triangle would this be, and what can you say about the lengths of the medians to these two corresponding sides?

3. ## 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.