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Mathematics · Grade 10

Parallel Lines and Coordinate Reasoning

Learners prove the angle relationships formed when a transversal crosses parallel lines and use their converses to prove lines parallel. They connect parallel and perpendicular lines to slopes, write equations of such lines, use the distance and midpoint formulas, partition segments in a given ratio, and write coordinate proofs that classify triangles and quadrilaterals.

  • 4 lessons
  • About 125 minutes
  • Parallel lines and coordinates check: 11 questions
  • Ways to answer: choose an answer, draw a graph, plot points, match pairs, type a number and put in order
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What learners will discover

  • Identify angle pairs formed by a transversal, prove the parallel-line angle theorems from the corresponding angles postulate, and use their converses to prove lines parallel.
  • Use slopes to decide whether lines are parallel or perpendicular and write equations of parallel and perpendicular lines through a given point.
  • Use the distance and midpoint formulas and find the point that partitions a segment in a given ratio.
  • Write coordinate proofs to classify triangles and quadrilaterals and compute perimeters and areas on the coordinate plane.

Lessons

  1. Transversals and angle pairs 7 steps5 practiceabout 32 min
  2. Slopes of parallel and perpendicular lines 6 steps4 practiceabout 30 min
  3. Distance, midpoint and partitions 7 steps5 practiceabout 30 min
  4. Coordinate proofs 7 steps4 practiceabout 30 min
  5. Parallel lines and coordinates check 11 questions at the end

Keep exploring

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Guide for grown-ups