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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
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
Constructions that are impossible using only a compass and straightedge include Trisecting an angle Squaring a circle Doubling a cube
doubling the cube
No
To trisect a right angle form an equilateral triangle with one vertex at the right angle and then bisect that angle of the equilateral triangle. (It is impossible to trisect a general angle using only compass and straight edge - the right angle is a specific exception.)
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.
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.
A compass and a straightedge