IM Geo.3.13 Lesson: Using the Pythagorean Theorem and Similarity

[size=150]Is triangle [math]ADC[/math] similar to triangle [math]CDB[/math] in the applet below? Explain or show your reasoning.[/size]
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.[br]
Determine the scale factor for each pair of triangles.
Determine the lengths of sides [math]HG[/math], [math]GF[/math], and [math]HF[/math].
Convince yourself there are 3 similar triangles. Write a similarity statement for the 3 triangles.[br]
Write as many equations about proportional side lengths as you can.[br]
What do you notice about these equations?[br]
In the applet below, Tyler says that since triangle [math]ACD[/math] is similar to triangle [math]ABC[/math], the length of [math]CB[/math] is 11.96. Noah says that since [math]ABC[/math] is a right triangle, we can use the Pythagorean Theorem. So the length of [math]CB[/math] is 12 exactly. Do you agree with either of them? Explain or show your reasoning.
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Information: IM Geo.3.13 Lesson: Using the Pythagorean Theorem and Similarity