Step-by-step explanation:
For the thir column we are told that the reason for the statement that sould be on the first column is related to the definition of a bisector, a perpendicular bisector of a line segment divides it into two equal parts, that is, the bisector PM divides AB into AM and MB, then the third statement is:
In the fourth row of the table, we are told that PM ≅ PM, this statement is formulated because when the bisector is drawn two right triangles can be formed, like this:
Then, the reason for PM≅PM is that this is a common side for both figures.
These triangles have two pairs of congruent sides ( PM≅PM and AM≅MB) and one pair of congruent angles (mΔAMB ≅ ΔBMP, and the rason is: SAS theorem.
Since these two triangles are congruent, the corresponding pair of sides PA and PB are congruent sides, then the last statement is: PA ≅ PB, the reason is: corresponding sides of a pair of congruent angles have the same length.