How do I prove that the ray drawn bisects the angle?

Place the compass point at one end of the arc. Strike arcs of a given radius on each side of the circle's arc. Place the compass point at the other...

Treat the arc as if it were a straight line segment, and perform the operation shown in the article above. You can also strike arcs only on the outside of...

Let's assume you want to bisect a 60° angle using a compass and straightedge. Place the point of the compass at the 60° angle's vertex. Strike an arc through the...

One.

This is more a matter of intuition than proof. It's the subject of Euclid's Parallel Postulate. It's considered an axiom and has been the subject of much controversy for centuries.

Yes, your suggestion will work. You also may find Method 3 to be less confusing than the other methods shown. Method 3 is just a variation of the method you're...

When you make the first arc, at points x and y in this article, you are actually marking the lengths of two sides of a triangle. When you draw the...

That is correct. The vertex of an inscribed angle is on the outside of a circle. When an inscribed angle and a central angle share the same arc on a...

Take the 90, add it to 35. This gives you 125 degrees. Triangles can only ever add up to 180, thus take the difference of 125 and 180 (180-125). This...

A right angle triangle always consists of one 90 degree angle, and every triangle must equal 180 degrees. Here is the work for this problem: 90 degrees (representing the right...