Can you divide ANY obtuse angle into two equal parts?

Answer 1

Short answer: Yes.

In fact all angles (right, accute or obtuse) can be divided into two equal parts. Here's a mathematical proof for all the angles measuring more than 0 degrees:

This is our setup: Let A, B and C be three points. Let H be a half plane bounded by the line AB, and let C lie in the half plane H.

Now, let the rays AB and AC define the angle r . It is postulated (in "The Protractor Postulate") that for every non-negative real number less than 180, call it k, and for every half plane bounded by the line AB, there exist a unique ray AD such that D lies in H and u(k. Let k be a number such that k< r. From the "Betweenness theorem of rays" we now know that the ray AD lies between the rays AB and AC. From "The Protractor Postulate" we also know that if the ray AD is between the rays AB and AC, then u(k to be exactly r/2 (which indeed is less than r), we see that u(r - r/2 = r/2 = u(

Postulates are assumed truths in mathematics.

A theorem is a statement proven true by use of logical reasoning, ultimately based on the assumed truth of one or more postulates.

The terms point, half plane, lie in, ray, line, angle and angle measure are terms defined with ultimate presicion, leaving no doubt for the logics of the argument. Use a good textbook to study such definitions and concepts. Gerard. A. Venema - "Foundations of Geometry" is the one I used to gather definitions and other details for this proof.