8.MATH.8.D

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

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Vocabulary
informal argumentsfactsangle sumexterior angletrianglesanglesparallel linestransversalangle-angle criterionsimilaritycriterion
Skills
  • establish (facts about the angle sum and exterior angle of triangles) #dok2
  • explain (angles created when parallel lines are cut by a transversal) #dok2
  • use (angle-angle criterion for similarity of triangles) #dok2
  • justify (facts about angles and similarity of triangles using informal arguments) #dok3
Learning Targets
  • I can describe the relationships of angle sums and exterior angles in triangles. #dok1
  • I can recognize and state facts about angles formed when parallel lines are cut by a transversal. #dok1
  • I can identify the angle-angle criterion for similarity of triangles. #dok1
  • I can use informal arguments to establish facts about the angle sum and exterior angle of triangles. #dok2
  • I can use informal arguments to explain the angles created when parallel lines are cut by a transversal. #dok2
  • I can demonstrate how the angle-angle criterion determines similarity in triangles using arguments. #dok2
  • I can justify why certain facts about angles and similarity of triangles are true using informal reasoning. #dok3
Big Ideas
  • Geometric relationships such as angle sums, exterior angles, and similarity can be established and justified using reasoning.
  • Understanding properties of triangles and parallel lines is foundational to solving more complex geometric problems.
Essential Questions
  • How can we use reasoning to prove relationships among angles in triangles?
  • What happens to angle measures when parallel lines are cut by a transversal?
  • Why does the angle-angle criterion guarantee similarity between triangles?
  • How can informal arguments help us recognize and explain geometric properties?
  • In what situations is being able to justify geometric facts important?