In a subsequent lesson, students will use the altitude to the hypotenuse of a right triangle to prove the Pythagorean Theorem. An altitude in a triangle is a line segment from a vertex to the opposite side that is perpendicular to that side. This lesson sets the stage for that proof by supporting students to make sense of the similar triangles formed by drawing the altitude to the hypotenuse of a right triangle. Students also get a chance to practice using the Pythagorean Theorem, equivalent ratios, and scale factors to find unknown side lengths in similar right triangles.
Students have a chance to reason abstractly and quantitatively (MP2) as they reason about angles in the triangles formed by drawing the altitude to the hypotenuse of a right triangle using tracing paper, measurement, and logical and algebraic reasoning.
Lesson overview
 13.1 Warmup: Similar, Right? (5 minutes)
 13.2 Activity: Tangled Triangles (15 minutes)

13.3 Activity: More Tangled Triangles (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 13.4 Cooldown: Finding Unknown Values in Right Triangles (5 minutes)
Learning goals:
 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).
Learning goals (student facing):
 Let’s explore right triangles with altitudes drawn to the hypotenuse.
Learning targets (student facing):
 I can find similar triangles formed by the altitude to the hypotenuse in a right triangle.
Required materials:
 Fourfunction calculators
 Protractors
Required preparation:

Ensure geometry toolkits are well stocked with tracing paper.
Glossary:
 altitude  An altitude in a triangle is a line segment from a vertex to the opposite side that is perpendicular to that side.
 Access the complete Geometry Course glossary.
Standards:
 This lesson builds on the standard: CCSS.HSGSRT.A.3MS.GSRT.3MO.G.SRT.A.3
 This lesson builds towards the standard: CCSS.HSGSRT.A.3MS.GSRT.3MO.G.SRT.A.3
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