Quick Geometry Problem

This was in my textbook, didn't have to do it but eh.. I tried it and couldn't figure it out, so I showed my dad and he said it was impossible because A and W are not midpoints. Could some of you just verify that this problem is impossible to solve?



Given: Segment VX congruent to Segment VZ

Y is midpoint of Segment XZ

Prove: Segment WY is congruent to Segment YA

x339 in IRC:

 

You are not sure YW and YA are midpoints to VX and VZ respectively, neither are we sure if the 3 sides of the triangle are equal.

This is impossible.

 

I believe congruent includes the two middle points in segment VX and VZ so you know they are in the same place and since Y is the midpoint you know the two lines are the same.

 

But we are not sure W and A are actually midpoints?

 

If congruent means what I think it means, it means that W and A are in the same relative location so even if they are not in the center, they are in the same place. I could have congruence wrong but I doubt it.

 

Yes you have it right, but you need to remember you are trying to prove WY and YA are congruent, like you stated they would have to be in the same position, but in Geometry we can only now this if a Mid-point is depicted or them " dashes showing Length Ratios.

 

Y is a midpoint and the other two have the same ratio of where they are on the lines. That makes them fairly basically the same. >_>

 

Pardon me if I'm being stupid, but how would we know that W and A are relatively at the same place? There is no restriction that tells us that W or A couldn't be much higher up/lower down..

 

That was part of my point, thank you.