Question

(Math Help Quick Lots of points please thanks) 3 (look for 2nd picture too for bottom half of page)

Answer 1

Given:

`\overline{PX}\:is\: ⊥\:bisector\:of \:\overline{YZ}`

To prove:

`YP=ZP`

Proof:

`YX=XZ \\ \sf[Since \: PX \: is \: perpendicular \: bisector, \\ \sf\: both \: parts \: of \: the \: bisected \: line \: are \: equal]`

`ΔPXY ≅ ΔPXZ \\ \tt [by \: sss \: congruence \: rule]`

`YP = ZP \\ \bf \: [by \: CPCT]`

Answer 2

Given
`\overline{PX}` is the
`\perp` bisector of
`\overline{YZ}`

⇒
`\overline{YX}` =
`\overline{XZ}`

⇒ ΔPXY ≅ ΔPXZ

⇒ YP = ZP

Explanation:

Given
`\overline{PX}` is the
`\perp` bisector of
`\overline{YZ}`

⇒
`\overline{YX}` =
`\overline{XZ}`

⇒ ΔPXY ≅ ΔPXZ

⇒ YP = ZP