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?

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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?

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Answer 1 · 2015-11-24T04:07:00

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.

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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

Explanation:

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