Question

What are the missing parts that correctly complete the proof

Given: Point P is the perpendicular bisector of AB
Prove: P is equidistant from the endpoints AB
Drag the answers into the boxes to correctly complete the proof
1. Point P is on the perpendicular bisector of AB given
2.__definition of bisector
3. 4.__all angles are congruent
5.PX=PX reflexive property of congruence
6.__SAS congruency postulate
7.__ corresponding parts of congruent triangles are congruent
8. Point P is equidistant from the endpoints of AB definition of equidistant

Answer 1

1 congruent segments

2 perpendicular lines

3 reflexive property

4 CPCTC

Explanation:

Enginuity says its right

Answer 2

2.
`\overline{AX}\cong \overline{BX}`

3.
`PX \perp AB` - definition of perpendicular

4.
`\angle PXA \cong \angle PXB` - all right angles are congruent

6.
`\triangle AXP\cong \triangle BXP`

7.
`\overline{PA} \cong \overline{PB}`

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.
`\overline{AX}\cong \overline{BX}` - definition of bisector

3.
`PX \perp AB` - definition of perpendicular

4.
`\angle PXA \cong \angle PXB` - all right angles are congruent

5.
`\overline{PX} \cong \overline{PX}` - reflexive property of congruence

6.
`\triangle AXP\cong \triangle BXP` - SAS congruency postulate

7.
`\overline{PA} \cong \overline{PB}` - corresponding parts of congruent triangles are congruent

8. Point P is equidistant from the endpoints of AB - definition of equidistant