I Don't Understand Proofs...10 pts!!?

Question

Can someone please show me an example just by showing the statements?

Given: S is the midpoint of segment RT
AX=ST
XP=RS

Prove: X is the midpoint of segment AP

Answer 1

Draw two lines, not necessarily parallel
On Line 1. , call it RT. Designate the mid-point of this line as S.

On Line 2., call it AP. Designate what you THINK is the mid-point of the line as X

Now here's what you were after. Refer to your drawing to keep things clear in your mind.

GIVEN: Straight line RT, with mid-point S
............ Straight line AP, with interior point X
..............AX = ST
..............XP = RS

REQUIRED TO PROVE: X is the mid-point of AP

PROOF: S is the mid-point of RT (given)
...............Therefore RS = ST
................But AX= ST (given)
................Therefore AX = RS
Also, XP = RS (given)
Therefore XP = AX
Therefore X must be mid-point.
That's it. We are done!

Answer 2

Basically, you show that AX=XP SINCE things equal to a third thing are equal to each other.

Once we buy that, X is at the midpoint by definition of a bisector.