Lesson 15
Finding All the Unknown Values in Triangles
Lesson Narrative
This lesson invites students to practice the strategies they have used to find unknown lengths in similar right triangles. A key strategy for students to practice in this lesson is using proportional relationships within similar triangles to find unknown lengths in other triangles. In a subsequent unit students will study trigonometry through similar right triangles, and the ratios in trigonometry tables are ratios within triangles.
The Info Gap routine requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).
Learning Goals
Teacher Facing
 Use similarity, proportionality, and the Pythagorean Theorem to solve problems involving right triangles (using words and other representations).
Student Facing
 Let’s find all the unknown values in right triangles.
Required Materials
Required Preparation
The origami paper is for use in the extension problem of the activity Relatively Reasonable.
Learning Targets
Student Facing
 I can solve problems involving similar right triangles.
CCSS Standards
Glossary Entries

altitude
An altitude in a triangle is a line segment from a vertex to the opposite side that is perpendicular to that side.