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Congruence and Proportions in Similar Triangles - Lesson 8-4

Today, we applied the definition of similar polygons to solve some interesting problems...for instance, we started with a "shadow" problem:

We recognized that we could draw in two similar triangles (why are the similar?) and then set up proportions from these to solve for the tree's height (you should be able to see that it is 30' tall):

We then did this example proof, which shows how you can your the Means-Extremes Products Theorem to prove a relationship between the segments shown: