Question

Complete the missing parts of the paragraph proof. Draw a perpendicular from P to AB. Label the intersection C. We are given that PA = PB, so PA ≅ PB by the definition of . We know that angles PCA and PCB are right angles by the definition of . PC ≅ PC by the . So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by . Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of perpendicular bisector.

Answer 1

1) congruent segments

2)perpendicular lines

3)reflexive proterty

4)CPCTC

Answer 2

The triangle ACP is congruent to triangle BCP by HL (Hypotenuse-Leg) congruence, and AC ≅ BC by CPCTC (Corresponding Parts of Congruent Triangles).

The completed paragraph proof:

Given:

PA = PB

Prove:

P is on the perpendicular bisector of AB

Proof:

Draw a perpendicular from P to AB. Label the intersection C.

We are given that PA = PB, so PA ≅ PB by the definition of congruence.

We know that angles PCA and PCB are right angles by the definition of a perpendicular.

PC ≅ PC by the reflexive property of congruence.

So, triangle ACP is congruent to triangle BCP by HL (Hypotenuse-Leg) congruence, and AC ≅ BC by CPCTC (Corresponding Parts of Congruent Triangles)

Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of perpendicular bisector.