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?

1 Answer
Nov 24, 2015

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.