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).
Lesson overview
 15.1 Warmup: Which One Doesn’t Belong: Triangles (5 minutes)
 15.2 Activity: Info Gap: Similar Sequence (20 minutes)

15.3 Activity: Relatively Reasonable (10 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 15.4 Cooldown: Calculate and Check (5 minutes)
Learning goals:
 Use similarity, proportionality, and the Pythagorean Theorem to solve problems involving right triangles (using words and other representations).
Learning goals (student facing):
 Let’s find all the unknown values in right triangles.
Learning targets (student facing):
 I can solve problems involving similar right triangles.
Required materials:
 Fourfunction calculators
 Origami paper
 Preprinted cards, cut from copies of the blackline master
Required preparation:
 The origami paper is for use in the extension problem of the activity Relatively Reasonable.
Standards:
 This lesson builds on the standard: CCSS.8.G.B.7MS.8.G.7MO.8.GM.B.7
 This lesson builds towards the standard: CCSS.HSGSRT.C.8MS.GSRT.8MO.G.SRT.C.7
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