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3 years ago

What are the missing parts that correctly complete the proof

Mathematics

1 answer:

bonufazy [111]3 years ago

5 0

Answer:

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. $\overline{PA} \cong \overline{PB}$

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. $\overline{AX}\cong \overline{BX}$ - 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

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