Answer:
#1) Angle Addition Postulate; #2) Definition of bisect; #3) postulate, definition and conjecture; #4) Given, Segment Addition Postulate, Subtraction Property of Equality; #5) Angle Addition Postulate, 60°+40°=m∠ABC, 100°=m∠ABC, Definition of obtuse angle.
Explanation:
The angle addition postulate says that when two angles have a common vertex and common side, the measures of the smaller two angles added together is equal to the measure of the larger angle formed by the two. In Statement 3 of Problem 1, JMK and KML are added to form JML. This is the angle addition postulate.
When a segment or a line bisects an angle, it cuts it into two equivalent angles. This is why the angles formed by bisector PQ, RPQ and QPS, are congruent.
Postulates, definitions, conjectures and theorems can all be used as reasons in a two-column proof. Premises are not.
In #4, we are given that KL = MN. LN is formed by pieces LM and MN; this is the segment addition postulate. Once we have KL+LM = LM+MN, we can subtract LM from both sides; the property that allows us to do this is the subtraction property of equality.
In #5, we see that ∠ABC is formed by angles ABD and DBC; this is the angle addition postulate. ABC = 60° and DBC = 40°; we substitute these in for the angles, using the substitution property. We can then add these two angles together for a measure of 100°. This is by definition an obtuse angle.