Answer:
2. [tex]\overline{AX}\cong \overline{BX}[/tex]
3. [tex]PX \perp AB[/tex] - definition of perpendicular
4. [tex]\angle PXA \cong \angle PXB[/tex] - all right angles are congruent
6. [tex]\triangle AXP\cong \triangle BXP[/tex]
7. [tex]\overline{PA} \cong \overline{PB}[/tex]
Step-by-step explanation:
Given: Point P is the perpendicular bisector of AB
Prove: P is equidistant from the endpoints AB
Proof.
1. Point P is on the perpendicular bisector of AB - given
2.[tex]\overline{AX}\cong \overline{BX}[/tex] - definition of bisector
3. [tex]PX \perp AB[/tex] - definition of perpendicular
4. [tex]\angle PXA \cong \angle PXB[/tex] - all right angles are congruent
5. [tex]\overline{PX} \cong \overline{PX}[/tex] - reflexive property of congruence
6. [tex]\triangle AXP\cong \triangle BXP[/tex] - SAS congruency postulate
7. [tex]\overline{PA} \cong \overline{PB}[/tex] - corresponding parts of congruent triangles are congruent
8. Point P is equidistant from the endpoints of AB - definition of equidistant
