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MathidiaMathematics Academy
Angle reasoning and constructions
Lesson 45 of 75
Review

Bisectors and constructions

Objective. Construct perpendicular and angle bisectors accurately.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Bisectors and constructions develops a connected mathematical idea rather than an isolated trick. Build chains of geometric reasoning from angle facts. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

Which construction finds points equidistant from two points?

perpendicular bisector
Illustrated card showing perpendicular bisector
  1. 1Identify the known information, the unknown and any conditions.
  2. 2Choose a diagram, table, graph or algebraic representation that exposes the structure.
  3. 3Apply the relevant rule one justified step at a time, keeping exact values where useful.
  4. 4Check by substitution, inverse reasoning or estimation. The result is perpendicular bisector.

Answer: perpendicular bisector

Concept mastery

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Practice

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Common mistake. A common error in bisectors and constructions is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

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