MMA.MATH.6.C

Use the Pythagorean Theorem and special right-triangle relationships to calculate distances.

Mathematical Models with Applications · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
Pythagorean Theoremspecial right-triangle relationshipsdistancesright triangleleghypotenusetrianglegeometry
Skills
  • apply (Pythagorean Theorem to calculate distance) #dok2
  • identify (special right-triangle relationships in geometric contexts) #dok1
  • solve (for missing side lengths using right triangle relationships) #dok2
  • calculate (distances using geometric and algebraic methods) #dok2
  • analyze (problems to determine when to use Pythagorean Theorem or special triangle properties) #dok3
Learning Targets
  • I can identify right triangles and label their legs and hypotenuse. #dok1
  • I can recognize special right triangles (such as 30-60-90 and 45-45-90) in geometric figures. #dok1
  • I can use the Pythagorean Theorem to calculate the length of an unknown side in a right triangle. #dok2
  • I can apply special right-triangle relationships to quickly solve for side lengths without calculation. #dok2
  • I can solve real-world problems involving distances by selecting and justifying the use of the Pythagorean Theorem or special right triangle rules. #dok3
  • I can analyze a geometric situation to determine if the Pythagorean Theorem or a special right triangle relationship is the most efficient strategy. #dok3
Big Ideas
  • The Pythagorean Theorem and special right-triangle relationships provide efficient methods for calculating unknown distances in geometric contexts.
  • Recognizing when and how to apply geometric theorems and patterns supports problem solving in architecture, engineering, and everyday situations.
Essential Questions
  • How can the Pythagorean Theorem be used to find distances in the real world?
  • What are special right-triangle relationships, and how do they make solving problems easier?
  • When should you use the Pythagorean Theorem versus a special right triangle approach?
  • How do geometric relationships help solve problems in architecture and engineering?
  • What must you look for to decide which mathematical relationship best applies to a given problem?