GEOM.MATH.6.A

Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems.

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

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Vocabulary
theoremangleintersectionlineline segmentvertical anglesparallel linestransversalequidistanceendpointssegmentperpendicular bisectorrelationshipsproblems
Skills
  • verify (theorems about angles formed by intersecting lines and segments) #dok2
  • identify (vertical angles and angles formed by parallel lines cut by a transversal) #dok1
  • prove (equidistance between endpoints of a segment and points on its perpendicular bisector) #dok3
  • apply (angle and segment relationships to solve problems) #dok3
Learning Targets
  • I can identify vertical angles formed by the intersection of two lines. #dok1
  • I can recognize angles formed by parallel lines cut by a transversal. #dok1
  • I can verify theorems about angles created by intersections of lines and segments. #dok2
  • I can justify relationships involving vertical angles and angles from parallel lines with a transversal. #dok2
  • I can prove that points on the perpendicular bisector of a segment are equidistant from the segment's endpoints. #dok3
  • I can apply theorems about angles and segments to solve geometric problems. #dok3
Big Ideas
  • Relationships among angles formed by intersecting lines and parallel lines are fundamental properties that can be proved and used to solve geometric problems.
  • Understanding and applying theorems about equidistance and angle relationships strengthens reasoning and deductive proof skills in geometry.
Essential Questions
  • What types of angles are formed when two lines intersect?
  • How can we prove angle relationships when parallel lines are cut by a transversal?
  • What does it mean for points on the perpendicular bisector of a segment to be equidistant from the endpoints?
  • How can we justify geometric claims through verification and proof?
  • In what ways can these theorems help us solve real-world or complex geometric problems?