7adv.MATH.10.H

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Grade 7 (Advanced) · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
informal argumentsfactsangle sumexterior angletrianglesanglesparallel linestransversalangle-angle criterionsimilaritytriangles
Skills
  • establish (facts about angle sum and exterior angle of triangles) #dok3
  • establish (facts about angles created when parallel lines are cut by a transversal) #dok3
  • establish (facts about the angle-angle criterion for similarity of triangles) #dok3
  • use (informal arguments to support understanding of geometric relationships) #dok3
Learning Targets
  • I can use informal arguments to explain why the sum of the angles in a triangle is a specific value. #dok3
  • I can use informal arguments to show relationships between the exterior angle and the remote interior angles of a triangle. #dok3
  • I can justify angle relationships formed when parallel lines are cut by a transversal using informal arguments. #dok3
  • I can explain and justify the angle-angle criterion for the similarity of triangles using informal reasoning. #dok3
Big Ideas
  • Geometric relationships can be understood and justified through informal arguments, not only formal proofs.
  • Understanding the underlying reasons for geometric facts deepens mathematical comprehension and problem-solving skills.
Essential Questions
  • How can we use informal arguments to explain why the angles of a triangle always add to a certain value?
  • What is the relationship between exterior angles and remote interior angles of a triangle, and how can we reason about it?
  • How do the angles formed when parallel lines are cut by a transversal relate to each other, and can we justify these facts using reasoning?
  • What does the angle-angle criterion for triangle similarity mean, and why does it work?
  • Why is it valuable to be able to justify geometric facts using informal arguments as well as formal proofs?