Question

What are the missing parts that correctly complete the proof?

Answer 1

Please see below.

Explanation:

(1) As `BP` is the bisector of `/_ABC`.

(2) `/_BXP=/_BYP`

(3) `BP` is common to both triangles.

(4) Congruence as `A AS`.

(5) `PX=PY`

Answer 2

Please see below.

Explanation:

1. Definition of an angle bisector.
   `color(white)a`
2. `/_ BXP~= /_BYP`
   `color(white)a`
3. Reflexive property
   `color(white)a`
4. AAS
   `color(white)a`
5. `bar(XP)~= bar(YP)`