In `DeltaPQR` seg PM is a median. Angle bisectors of `/_PMQ` and `/_PMR` interesect side PQ and side PR in points X and Y respectively. Prove that `XY||QR`.
Complete the proof byfilling in the boxes:

Explanation

In `DeltaPMQ` ray MX is bisector of `/_PMQ`
`:.(square)/(square)=(square)/(square)`
……….(Theorem of angle bisector)……………I
In `DeltaPMR`, ray MY is bisector of `/_PMR`.
`:.(square)/(square)=(square)/(square)`
…………(Theorem of angle bisector ).............II
But `(MP)/(MQ)=(MP)/(MR)M` is the midpoint of QR,
hence `MQ-MR`
`:.(PX)/(XQ)=(PY)/(YR)`
`:.XY||QR`....(Converse of basic proportionality theorem)
Proof: In `Delta PMQ`, ray MX is bisector of `/_PMQ`
`:.(PM)/(MQ)=(PX)/(XQ)`
........(Theorem of angle bisector ) .............I
In `DeltaPMR` ray My is bisector of `/_PMR`.
`:.(PM)/(MR)=(PY)/(YR)`
...(Theorem of angle bisector ) .......II
But `(MP)/(MQ)=(MP)/(MR)M` is the midpoint of QR,
Hence `MQ=MR`
`:.(PX)/(XQ)=(PY)/(YR)`
`:.XY||QR`. (Converse of basic proportionality theorem)