**Prove: The altitudes of a triangle are
concurrent.**

**Click here
for a GSP 4.0 sketch to manipulate.**

Given triangle ABC, we wish to demonstrate that altitudes BF, AE and CD are concurrent.

Note that

Similarly,

and

By substitution,

After cancellation,

and by the converse of Ceva's theorem, we have demonstrated that altitudes AE, BF and CD of triangle ABC are concurrent.