Unit 3, Lesson 13
Using the Pythagorean Theorem and Similarity
Geometry
Preparation
Lesson Narrative
In this lesson, students examine a particular diagram of a right triangle with an altitude drawn to the hypotenuse. An altitude is a line segment in a triangle that connects a vertex to the opposite side so that it is perpendicular to that side. Students should notice that this altitude creates triangles that are similar to the original right triangle. They must reason abstractly and quantitatively to verify the similarity of the triangles, using a variety of tools (MP2).
Students also practice using the Pythagorean Theorem along with equivalent ratios or scale factors to find unknown lengths.
- Justify that the two smaller right triangles formed when a right triangle has an altitude drawn to its hypotenuse are similar to the original right triangle (in writing).