AQR.MATH.2.D

Solve geometric problems involving indirect measurement, including similar triangles, the Pythagorean Theorem, Law of Sines, Law of Cosines, and the use of dynamic geometry software.

Advanced Quantitative Reasoning · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
geometric problemsindirect measurementsimilar trianglesPythagorean TheoremLaw of SinesLaw of Cosinesdynamic geometry software
Skills
  • solve (geometric problems involving indirect measurement) #dok3
  • apply (similar triangles to solve measurement problems) #dok2
  • use (the Pythagorean Theorem in real-world and abstract situations) #dok2
  • apply (Law of Sines and Law of Cosines to solve for missing values in triangles) #dok2
  • utilize (dynamic geometry software to model and solve geometric problems) #dok3
Learning Targets
  • I can identify situations requiring indirect measurement in geometric problems. #dok1
  • I can recall and state the properties of similar triangles, the Pythagorean Theorem, Law of Sines, and Law of Cosines. #dok1
  • I can select the appropriate theorem or law for solving a particular geometric measurement problem. #dok2
  • I can apply similar triangles or the Pythagorean Theorem to find missing measurements. #dok2
  • I can use the Law of Sines and Law of Cosines to solve for unknown angles or sides in triangles. #dok2
  • I can model and solve geometric problems using dynamic geometry software and explain my process. #dok3
  • I can solve real-world or theoretical problems by integrating multiple geometric concepts and justifying my solutions. #dok3
Big Ideas
  • Indirect measurement techniques allow us to solve geometric problems when direct measurement is not possible.
  • Understanding and applying relationships in triangles unlocks solutions to a variety of real-world and abstract problems.
Essential Questions
  • How can geometric principles help us solve problems when direct measurement is impossible?
  • In what situations would you use similar triangles, the Pythagorean Theorem, or trigonometric laws for measurement?
  • How does the use of technology, such as dynamic geometry software, enhance problem-solving in geometry?
  • What reasoning helps you decide which geometric concept or method to apply to an indirect measurement problem?
  • How can you justify your solution process when solving complex geometric problems?