Special Lines in Triangles: Bisectors, Medians, and Altitudes

What's a median? Or an altitude? They are special lines you can make with a triangle. And what's a circumcenter, or a centroid, or an orthocenter? These are some special points that relate to triangles. Not every geometry course covers this terminology, but it's super interesting, so take a look!

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[kaiserquasar]

I loved it when professor Dave went "it's geometrying time" and then geometried all over the place, truly one of the moments of all time.

[AJ-fohp]

In center---- Angle bisector
Centriod ---- Intersection of 3 median ( bisector for side drawn from opposite angle)
Orthocenter---- Altitude (perpendicular line drawn from from opposite angle)
Circumcenter----3 perpendicular bisector drawn

[ruvstof]

Thank you. I am studying philosophy of space and time. Good to revise things I should have learned many years ago.

[Carrymejane]

I actually just using ur video as a start point for learning something and as a summary of " did i already understand this?" Because somehow i should have learn in other resources to understand a whole 1 video and that's not ur fault, I'm gladly thank because u make these playlist so it can be my roadmap for math journey. Thanks professor dave ❤

[davidvolland]

This is excellent a perfect summary gioving all the facts to understand all 3, it moves quickly so you may need to pause or review. But it beats someone going on and on for 45 minutes and trying not to get bored and fast forward or skip. Like Joe Friday said, "Just the facts nothing but the facts"

[bernadettem]

Thank you! This will help me prepare for my math test on Monday

[kai.acadventure]

Hello, I'm a learner from Vietnam. I'm following your series as I want to prepare mathematical knowledge for my abroad study, and I find them very helpful. However in this video there seems to be a little awkward problem. When it comes to the Perpendicular Bisector, the way you visualize it in the first part of the video make me feel like Perpendicular Bisector just only exists in Isosceles Right Triangle. I think it's not always the case. ^^ Anyway, thank you for your videos!!!

[ReimskyToussaint]

Anticipated thanks to use this excellent little theory quiz at the end in my Geometry class in the future. Great vid.

[ReimskyToussaint]

At 2:26, I would add/mention a few things.
- I would add right angle symbols at those little pink segments of distance.
- I would expand on "distance", explaining that the distance from two points is the length the segment connecting them, while the distance from a point to a line (or segment) is the perpendicular segment to that line that originates from that point. Thus the three sides of the triangle here are equidistant ("equal distance") from the incenter since these three pink segments of distance are of same length.

Great video as always.

[frankines]

Love your videos!! They are a really good resource for learning. Thanks a lot!

[audiesamuel]

It is difficult to keep track of what I'm doing this helped me alot.

[RayverRegelisa]

This was discussed in our lecture during the Philippine Mathematical Olympiad Training Sessions. Tried studying it again through YouTube since I'm not familiar with the terms yet lol.

[frayedendsofsanity]

I'm in med school.. Why am I watching this lol

[Blacksoul]

Thank you very much for the compact explanation!

Oh, btw. At 0:43, dont you mean isosceles triangle instead of right triangle?
If the perpendicular bisector of the base interesects with the other 2 sides (and therefore ultimately is the altitude of the base), we know that the other 2 sides have the same lengths. Therefore it is definitely an isosceles triangle. But it does not necessarily have to have 90 degrees at the intersection and we cannot say for sure that it is a right triangle, right?

[panchi]

0:41 isn't that an isosceles triangle instead of a right one?

[rahulchittur]

Congratulations! U have 100k subscribers.

[chasethescientistsaturre]

Thank you dude. I'm advance to all of my classmates thanks to you.

[dableuyoshiemu]

Suppose I take a point from the angle bisector, according to this video it is supposed to be equidistant from both sides, but at what angle should I draw the equidistant line from the angle bisector? That part was a little vague for me...

[jasonruzicka]

"Here lays the problem with your model....YOU DON'T HAVE ONE!"
~ Professor Dave

[rajeshannamdevula]

Do we define perpendicular bisectors or medians only in a triangle?