The answer is noun:gerund::adjective:participle
First, it is important to identify the relationship between the first pair of words. A gerund is a noun that came from a verb by the addition of the suffix "-ing". In short, it is a verbal noun. For example: "Walking is a good way to be healthy."
For the second pair, the same relationship must be followed. A participle is an adjective that came from a verb by the addition of "-ing, -en, -ed or -t" as well. In short, it is a verbal adjective. For example: "I need walking shoes."
