Learn Finnish: Talon katto on iso kolmio. - The roof of the house is a large triangle.

In Finnish, to express the roof OF the house, you use the genitive case, which acts like the English apostrophe-s. So Talon katto literally translates to the house's roof.

Since the roof is being described, why isn't the ending iso kolmio in the partitive case?

When you have an A is B sentence (a predicative sentence), the case of B depends on whether it is countable or uncountable. Because kolmio (triangle) is a single, countable thing, it stays in the basic nominative case. If it were an uncountable mass noun, it would take the partitive.

How does the sentence show it means THE roof and A large triangle without any translation for 'the' or 'a'?

Finnish doesn't have articles. Whether a noun is definite or indefinite is understood from context and word order. The subject at the beginning of the sentence is usually understood as definite (the roof), while new information introduced at the end is indefinite (a triangle).

Does the word kolmio come from the number three?

Yes! The root is kolme (three). The suffix -io is often used in Finnish to create a noun from another word. Adding it to the number three gives you a three-sided shape. You also see this pattern in neliö (square) from neljä (four).