IM Geo.3.13 Lesson: Using the Pythagorean Theorem and Similarity
Is triangle similar to triangle in the applet below? Explain or show your reasoning.
The two smaller triangles are copies of the ones that make up the biggest triangle. Convince yourself all 3 triangles are similar.
Write 3 similarity statements.
Determine the scale factor for each pair of triangles.
Determine the lengths of sides , , and .
Convince yourself there are 3 similar triangles. Write a similarity statement for the 3 triangles.
Write as many equations about proportional side lengths as you can.
What do you notice about these equations?
In the applet below, Tyler says that since triangle is similar to triangle , the length of is 11.96. Noah says that since is a right triangle, we can use the Pythagorean Theorem. So the length of is 12 exactly. Do you agree with either of them? Explain or show your reasoning.