Final answer:
To complete the proof, you need to provide the reasons for statements 3, 4, 6, and 7. Statement 3 can be proven by showing that ∠PXA and ∠PXB are right angles, as given in the information. Statement 4 follows from the definition of a right angle. Statement 6 can be proven using the Side-Angle-Side (SAS) Congruence Postulate. Statement 7 follows from the fact that corresponding parts of congruent triangles are congruent.
Step-by-step explanation:
To complete the proof, we need to fill in the reasons for statements 3, 4, 6, and 7.
Statement 3: ∠PXA and ∠PXB are right angles. Reason: The angle PXB is labeled as a right angle in the given information. Since point P is on the perpendicular bisector of segment AB, it is equidistant from points A and B. Therefore, ∠PXA is also a right angle as it subtends the diameter of a circle with P as the center and AX as the diameter.
Statement 4: All right angles are congruent. Reason: By definition of right angle.
Statement 6: SAS Congruence Postulate. Reason: Since APX and BPX are right triangles and PX is the common side, if we can show that ∠APX ≅ ∠BPX and AX ≅ BX, we can use the Side-Angle-Side (SAS) Congruence Postulate to establish that the two triangles are congruent.
Statement 7: Corresponding parts of congruent triangles are congruent. Reason: Once we have established that APX and BPX are congruent triangles, we can conclude that corresponding parts of those congruent triangles are congruent. Therefore, AX ≅ BX, which means that P is equidistant from the endpoints of segment AB.