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Goku is there once again to save the day for team Dragonball. These episodes mark the rest of the season, and is the primary theme for the rest of the series. Becoming a Super Saiyan at that moment was the critical point in the movie. Not only did he become Super Saiyan and had the strength to survive, but he also put an end to the madness of Frieza.

After these episodes, you get the feeling that if Goku is a Super Saiyan, is it hereditary? Would Gohan become the second legendary Super Saiyan after his father?

You'll find out in succeeding shows that Vegeta is infuriated and bitter that as a prince of all Saiyans, he can not become a Super Saiyan(...yet).

These episodes are critical in the story of Dragonball and you should try to see it, but also see the episodes that follow so you'll get the jist of it.