GEOM.MATH.9.B

Apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems.

Geometry · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
special right triangles30°-60°-90° triangles45°-45°-90° trianglesPythagorean theoremPythagorean triplesproblem
Skills
  • apply (relationships in 30°-60°-90° triangles) #dok2
  • apply (relationships in 45°-45°-90° triangles) #dok2
  • apply (Pythagorean theorem) #dok2
  • identify (Pythagorean triples) #dok1
  • solve (problems involving special right triangles and Pythagorean theorem) #dok3
Learning Targets
  • I can identify Pythagorean triples in right triangles. #dok1
  • I can recall the ratio of side lengths in a 30°-60°-90° triangle. #dok1
  • I can recall the ratio of side lengths in a 45°-45°-90° triangle. #dok1
  • I can apply the properties of 30°-60°-90° triangles to find missing side lengths. #dok2
  • I can apply the properties of 45°-45°-90° triangles to find missing side lengths. #dok2
  • I can apply the Pythagorean theorem to determine missing side lengths in right triangles. #dok2
  • I can analyze a context to determine which special right triangle or method to use when solving a problem. #dok3
  • I can solve complex problems involving multiple right triangle concepts, such as combining special triangles and the Pythagorean theorem. #dok3
Big Ideas
  • Special right triangles and the Pythagorean theorem provide efficient methods for solving problems involving right triangles.
  • Recognizing and applying special triangle relationships simplifies finding missing measures in geometric figures.
Essential Questions
  • How can I identify and use the properties of special right triangles (30°-60°-90° and 45°-45°-90°) to solve problems?
  • In what situations should I use the Pythagorean theorem versus special right triangle relationships?
  • What are Pythagorean triples, and how can they help me solve right triangle problems more efficiently?
  • How do geometric relationships in right triangles connect to solving problems in real-world contexts?
  • How can I determine when to use special right triangle relationships to find missing measures?