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True
True
No, and the proof was provided by Wantzel in 1837.
Yes and the trisections will form 4 angles of 22.5
No
True
True
True
As a general rule, no.
No, and the proof was provided by Wantzel in 1837.
Yes and the trisections will form 4 angles of 22.5
No
You don't need advanced algebra to prove that it is impossible to trisect a line segment using only a straight edge and a compass: anyone knows that you will also need a pencil! And one you have that then there are plenty of easy ways to do it.
That's a classic problem that's been around for a very long time.It's been proven that it's not possible to trisect any angle in generalwith those tools, although there are a few specific angles, like aright angle, for which it can be done.
Yes! It is! I'm not perfectly sure how, but my father has, in fact, done this.
First things first, the actual statement isn't "you can't trisect an angle" but rather "you can't trisect one with only a compass and straightedge." Some angles can be easily trisected--a 90-degree angle trisects into 30-degree segments-but to do it you need a protractor. Anyway, to check your work measure the angle you trisected and divide by three. If your trisections match, you got it right.
It is indeed impossible to trisect an angle using only a [pair of] compass[es] and a straight edge.It is in fact possible:1) measure the angle2) divide this measure by three3) measure the angle found in part (2) inward from the outer edge of the main angle4) use the straight edge to draw the trisectorsit is!!!!!!!!!!!!!!!!!!