In Module 2, Topic D, students use their understanding of similarity and focus on right triangles as a lead-up to trigonometry. In Lesson 21, students use the AA criterion to show how an altitude drawn from the vertex of the right angle of a right triangle to the hypotenuse creates two right triangles similar to the original right triangle. Students examine how the ratios within the three similar right triangles can be used to find unknown side lengths.Work with lengths in right triangles lends itself to expressions with radicals.In Lessons 22 and 23, students learn to rationalize fractions with radical expressions in the denominator and also to simplify, add, and subtract radical expressions.In the final lesson of Topic D, students use the relationships created by an altitude to the hypotenuse of a right triangle to prove the Pythagorean theorem.

Content Standard(s):

Mathematics MA2015 (2016) Grade: 9-12 Geometry

17 ) Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [G-SRT4]