Proving AI = LI using Midpoint Postulate and Betweenness of Lines Theorem

[OrbitalPower]

I have a simple geometric proof (first proofs) I can't finish. Looks like this:

A________L


C________E

suppose there's a straight line from l to c and a to e (to make an x) and a midpoint I.

It says: Given I is the midpoint of both $$\overline{AE}$$ and $$\overline{LC}$$; AE = LC
Prove AI = LI

??

I'm not sure where to go except to start with the given. How do I complete (or start) the proof using the midpoint postulate and betweenness of lines theorem.

 

[arildno]

Now, you DO know that I is the MIDPOINT of each line segment.

Therefore, you know that:
AI=IE and LI=IC

Furthermore,

you have the equations:
AE=LC (given)
AI+IE=AE (betweenness of points)
LI+IC=LC (the same)

Now, can you jumble about these 5 equations to get your result?

 

[OrbitalPower]

AE = LC (given)
AI+ IE = AE (betweeness of points)
LI + IC = LC (the same)
AI=IE
LI=IC
Therefore AI = LI because AE = LC so the segments would be equal.

That's what i could come up with with those equestions.

 

[arildno]

At this level, your logic should be a bit more thorough than that.
Since IE=AI and IC=LI, we have:

2AI=AE and 2LI=LC
Thus, we get:
2AI=2LI, implying AI=LI