Why are there are several important similarities between Buddhism and Hinduism?

There just are not many substantial ways in which Hinduism and Buddhism are alike.

(1) They have their origins in the same country and time, and therefore in the same sets of questions about our place in the world and how we can best affect it. (Their answers, however, are quite opposite each other)
(2) They share some terms, however they use them in entirely different -- often totally opposite -- ways, so that's not "alike" but "contrary"
(3) They are both concerned with ethics
(4) They are both widely misunderstood by outsiders
(5) They are both interpreted in a wide variety of ways by their own practitioners.