G.1.2.3 Proves, directly or indirectly, that a valid mathematical statement is true. Develops a counterexample to refute an invalid statement. Determine the truth-value of a conditional statement in addition to its converse, inverse, and contrapositive by identifying counterexamples for statements with false truth-values. Dec 23, 2019 · An angle bisector divides an angle into 2 equal parts. The easiest way to construct a bisector of a given angle is with a protractor. First, measure the angle by placing the origin hole of the protractor on the angle’s vertex and lining up the baseline with one of the angle’s rays. Take the angle you get and divide this number by 2. We will take as given the following famous theorem: Theorem 1. (Angle Bisector Theorem). An angle bisector in a triangle divides the opposite side in the same ratio as the other two sides. More precisely, in ABC, if ray BD~ bisects \ABC, then AD : DC = AB : BC. A D C B Figure 7 Problem 11. In ABC, let AB = c, AC = b, and BC = a.