Triangle theorem? (1 Viewer)

[tacogym27101990]

hey sorry to ask a pretty silly question but:
is there a theorem or somehting i should no about the intersectionof the altitudes in a triangle from each vertices
will they always all intersect at the same point?
cause im doin a question and i proved it showing the intersection of all three altitudes
but the answer only used the intersection of 2 of the altitudes
and i vaguely remember seeing something like this???

thanks for ure help

 

[ronnknee]

Apparently there must be. I randomly drew two triangles and their respective altutides. It appears that they always intersect at one point. So my conclusion is: if two altitudes of a triangle intersect at a point, then the third altitude must pass through that point of intersection

I have nothing else to back myself up but that =p

 

[Affinity]

they do.. it's called the orthocenter you can prove it by some simple circle geometry.

Let 2 altitudes intersect at H, consider the line through H and the 3 vertex. prove that this is perpendicular to the corresponding base (there are many cyclic quadrilaterals in this figure)

 

[tacogym27101990]

thanks for your help guys
vaguely remembered something like that
but i wanted to make sure