triangle proportionality Theorem

What is the Triangle Proportionality Theorem?

In similar polygons, corresponding sides are ___ and corresponding angles are ___.

Select the correct proportion that shows the Triangle Proportionality Theorem: $$\frac{6}{27}=\frac{7}{x}$$ , $$\frac{6}{21}=\frac{7}{x}$$ , $$\frac{7}{6}=\frac{x}{27}$$

If two triangles are similar, what can be said about their corresponding angles?

If two triangles are similar, what can be said about their corresponding sides?

Find x in the proportion $$\frac{6}{21}=\frac{7}{x}$$ .

Find x in the proportion $$\frac{7}{x}=\frac{6}{27}$$ .

If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE are 6 and 9 respectively, what is the ratio of their corresponding sides?

If triangle ABC is similar to triangle DEF, and the length of side AC is 12, what is the length of side DF if the ratio of their corresponding sides is $$\frac{2}{3}$$ ?

What is the relationship between the areas of two similar triangles?