This can be taken as a self evident truth (axiom). It is possible the question in your book takes a different starting point of self evident truths and wants you to use logic to derive the equality of the two lengths.
Why can this be taken as a self evident truth?
Imagine walking x steps on a straight line and then rotating 90 degrees using your left hand and then taking y steps. OK, now go back to your starting point and facing the same direction take x steps and then rotate 90 degrees using your right hand and take y steps.
Now ask yourself what is the distance you traveled in both of these journeys. Well, you should feel no more tired in either case.
The attached picture should help.
Hint: By the way you phrased the question, you are dealing with an isosceles triangle. I was forced to draw the picture the way I did. You will certainly find this helpful:
The Isosceles Decomposition Theorem