Question

A conjecture and the paragraph proof used to prove the conjecture are shown.

Answer 1

Angle 2 is equal to angle 3, by definition of angle bisector. In fact, a line is an angle bisector if it cuts the angle in two equal angles, which in this case are 2 and 3.

Finally, we can state that angles 1 and 3 are the same by the transitive property of congruence, because we prooved that angle 1 equals angle 2 and angle 2 equals angle 3, so we can conclude that angle 1 equals angle 3.