Show that "halves of equals are equal" in the following sense: if $AB \cong CD$, and if E is a midpoint of AB in the sense that $A * E * B $ and $AE \cong EB$, and if F is a midpoint of CD, then $AE \cong CF.$
Conclude that a midpoint of AB, if it exists, is unique.
I am not really sure what this question is asking, at first i thought it was asking me to show that $AE \cong CF$ but perhaps its telling us that that is true and is asking us to show that the midpoint is unique? (i can show that the midpoint on AB is unique directly by assuming there are two of them and futzing around till i get a contradiction.
What am i being asked to show? and if im being asked to show that $AE \cong CF$ any ideas how to do so would be great.
Oh, I see. You don't have to prove it exist. But that if it does, it is unique.
So prove $A*E*B$ and $AE = EB$ and if $A*F*B$ and $AF = FB$ then $E=F$.
Hint: What is $AE + EB$ and what is $AF + FB$.
If $A*E*F*B$, what is $AE$ and what is $EF$ and what is $FB$? What happens if $AE =EB$? What does that say about $AF$ and $FB$?