Talk:Area of a Triangle in Terms of Circumradius

need a new title and i need someone who can write teh step of the contruction, my english isn't very good. the same // Gamma 03:09, 31 December 2008 (UTC)

I have problems with this page. My geometry is not good (I never studied it formally; in my education we went straight to analytic / coordinate geometry and never touched the traditional Euclidean variety). So I need explained:

• What is the construction that generates $D$?
• Having constructed $D$, why does "$\angle CAB \cong \angle CDB$ (cover the same arc)"?
• Does it make sense to say that two angles are "congruent" in the above, surely angles can be defined as "equal"?
• What is meant by "$(\widehat {CAD}=180)*$"?
• What is "by AA similarity"?
• I presume that (in the diagram) $O$ is the circumcenter. I believe this needs to be explained.

Apologies, but I believe the above may need to be addressed if this page is to be accessible to all. --Matt Westwood 11:24, 31 December 2008 (UTC)

• first one the contrucion of D generate de diameter a then we join D with C this step is for do a sim between triangle DBC and triangle AEC and with this we can write the altitude in terms of the circundiameter(circunradius)

well there a theorem that said that if we have n-inscribed-anlges have the same arc then those n-inscribed-angle are congruent see the figure above =)... i think i will do the proof soon...

• well this question im not sure what did yyou try to say but a thhink was the problems, why we use congrence and not equality... well first congruence if for "shapes" and equality is for value of length .. and think is like (Mod n) (sorry but a dont know a rigourous definition but is teh idea)

• $(\widehat {CAD}=180)*$ well that means that the arc CAD have the length equal to 180..

but what thsi means well if any inscribed-anlges cover this arc they will be equal to 90 º

• AA is the criterion Angle-angle thats means thats if tow traingle have 2 congruent angle then they are similary

• yes but my english isnt good and i dont have the best words for do a decent explanation of the contrucion i could try but i know this explanation will be wrong

-- Gamma 15:33, 31 December 2008 (UTC)

• I added a line on the construction of $D$

• It's a corollary to the Inscribed Angle Theorem

• Angles are congruent, measures of angles are equal. Saying two angles are equal implies that it is the same angle (not just the same measure). Silly, I know, but that's the way it goes.

• This needed more steps. Fix'd

• I learned AA Similarity as a postulate, I don't know what Euclid did. Anyway, it basically states that if triangle have two pairs of congruent angles, then they are similar. See wikipedia.

• I defined $O$ in the proof.

Sorry for duplicating what gamma said, I just wanted to make sure it was clear. I don't have a Euclidean Geometry text at my house, I'll see if I can borrow one from my school when I get back. --Cynic-----(talk) 01:21, 1 January 2009 (UTC)

Now I have all the technical terms explained it all makes sense. Okay to add a link to a page "Angle-Angle Similarity"? I don't think it needs to be a postulate as such, it follows directly (trivially) from the facts that (a) 3 angles of triangle add to 180 deg and (b) two triangles are similar if they have all the angles congruent.

Thanks for putting me straight on the definition of congruency for angles. As I say, I had a "modern" elementary mathematical education, we didn't do "trad" maths till whatever-grade-it-is when you're 16 and doing it in earnest. So no Euclid, but beaucoups of good old Descartes and Argand ... mind, I got my Euclid and been studying it on-and-off over the last few years, so I'm picking it up, just not good with the technical terminology. --Matt Westwood 01:38, 1 January 2009 (UTC)