Question

Segment AB contains points A, X, Y, and B. X is the midpoint of segment AY, and Y is the midpoint of segment XB. How would you prove that segment AX is congruent to segment YB?

Answer 1

See below.

Explanation:

Let the length of segment `AX` be `x`,
length of segment `XY` be `y` and
length of segment `YB` be `z`.

Then, since `X` is midpoint of `AY`,
`x = y`

Since `Y` is midpoint of `XB`,
`y = z`

From both of these equations we derive that, since `x=y` and `y=z`, then `x=z`.
So, segments `AX` and `YZ` have the same length. Therefore, they are congruent.