GEOM.MATH.2.B

Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines.

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

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Vocabulary
distance formulaslope formulamidpoint formulageometric relationshipscongruence of segmentsparallelismperpendicularitypairs of lines
Skills
  • derive (distance, slope, and midpoint formulas) #dok2
  • use (distance, slope, and midpoint formulas to verify geometric relationships) #dok2
  • verify (congruence of segments using formulas) #dok2
  • verify (parallelism or perpendicularity of pairs of lines using slope) #dok2
Learning Targets
  • I can recall the distance, slope, and midpoint formulas. #dok1
  • I can identify when to use distance, slope, and midpoint formulas for specific problems. #dok1
  • I can derive the distance, slope, and midpoint formulas from geometric definitions. #dok2
  • I can use the distance formula to verify if segments are congruent. #dok2
  • I can use slope to determine if lines are parallel or perpendicular. #dok2
  • I can use the midpoint formula to find the point halfway between two points. #dok2
  • I can justify the congruence or non-congruence of segments using calculations. #dok3
  • I can construct logical arguments about geometric relationships using coordinate formulas. #dok3
Big Ideas
  • Formulas for distance, slope, and midpoint are fundamental tools for analyzing and proving geometric relationships in the coordinate plane.
  • Understanding how to use and apply these formulas allows us to verify important properties such as congruence of segments and parallelism or perpendicularity of lines.
Essential Questions
  • How do you derive the distance, slope, and midpoint formulas from geometric concepts?
  • In what situations would you use the distance, slope, and midpoint formulas to verify geometric relationships?
  • How can you determine if two segments are congruent using coordinates?
  • How do you prove that two lines are parallel or perpendicular using their slopes?
  • Why is it important to verify geometric relationships using coordinate methods?