Need proof angle&segment bisect of a triangle are concur

[Jay-Naf]

Hello everyone,

I need a two colum proof that proves that the angle and perpendicular bisectors of a triangle are concurrent.

I need this ASAP.

Thx,

Jay

 

[stapel]

Maybe I'm missing something, but aren't "perpendicular bisectors" line segments? As such, they would have length. Angles are measured in degrees. How are lengths and degrees meant to be congruent?

Please reply with the full and exact text of the exercise. When you reply, please show the steps and reasoning you have tried thus far. Thank you.

Eliz.

 

[Jay-Naf]

umm concurrent not congruent

 

[stapel]

umm concurrent not congruent

Geez! I really need to clean my glasses! :roll: Sorry 'bout that.

Okay, but then my question becomes: What do we mean by "concurrent"? The perpendicular bisector of a given side will not necessarily be concurrent with the angle opposite (by which I mean that the segment will not necessarily end at the vertex of that angle).

Is the actual question something along these lines?

Prove that the angle bisectors of the three angles of any triangle intersect at one point. Prove that the perpedicular bisectors of the three sides of any triangle intersect at one point.

Note: The first concurrence is the "incenter" of a triangle; the second is the "circumcenter". These points are not necessarily the same (and, in fact, generally aren't). With these terms, though, you may have better luck finding information and guidance online, if applicable.

Again, my apologies for my earlier idiocy.

Eliz.