Vertical anglesDate: Tue, 15 Nov 1994 17:16:33 -0500 (EST) From: Anonymous Subject: QUESTION Dr. Math, Here is a question for you. Are vertical angles congruent in Euclidean geometry? Date: Tue, 15 Nov 1994 19:25:59 -0500 (EST) From: Dr. Ken Subject: Re: QUESTION Hello there! Boy, am I excited to answer your question! And I sound a resounding "YES!!" Vertical angles ARE congruent in Euclidean Geometry!! Do you see why this is true? I'll give you a hint: If you have a pair of vertical angles A and C, like this: | / | / | / | / | A / | / | / |/ | /| B / | / | / C | / | / | / | If the measure of angle A is x degrees, what is the measure of angle B? Then using the measure of angle B, what is the measure of angle C? It is a quite interesting fact that vertical angles in ANY (holy cow!) geometry are congruent. The proof is a little deeper, and since I don't have my Non-Euclidean Geometry book handy, I'll not give it to you right now, because I'd probably mess up. But if you're interested, let us know and I'll try to dig it up. I hope this helps! -Ken "Dr." Math |
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