I don't think you've been given enough information...
Can you find any of the shown segments? Also, a hint: use the right triangle altitude theorem.
Of course you are right but you also can use 2 right triangles to prove the altitude theorem:
(Using the labels of the attached diagram):
Add both equations columnwise:
Since the right side of the last equation becomes:
Collect like terms, divide through by 2 and you'll get the equation of the altitude theorem.