Yes! It is!
I'm not perfectly sure how, but my father has, in fact, done this.
True
True
No, and the proof was provided by Wantzel in 1837.
Yes and the trisections will form 4 angles of 22.5
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!!!!!!!!!!!!!!!!!!
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
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!!!!!!!!!!!!!!!!!!
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!!!!!!!!!!!!!!!!!!
False. It is not possible to trisect any arbitrary angle using only a compass and straightedge, as proven by Pierre Wantzel in 1837. While some specific angles can be trisected using these tools, the general case of angle trisection is one of the classic problems of ancient geometry that cannot be solved with these methods.
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.)
to construct an angle of 20 degrees all you have to do is to trisect an angle of 60degrees
To trisect a right angle, you first construct a 90-degree angle using a compass and straightedge. Then, draw an arc from the vertex of the angle that intersects both rays of the angle. Next, without changing the compass width, place the compass on each intersection point and draw arcs that intersect above and below the angle. Finally, connect these intersection points to the vertex, creating two lines that trisect the right angle into three equal 30-degree angles.
False. It is impossible to trisect any angle using only a compass and straightedge, as proven by Pierre Wantzel in 1837. While some angles can be trisected using these tools, the general case for all angles cannot be achieved through classical construction methods.