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MathidiaMathematics Academy
Pythagoras and right triangles
Lesson 56 of 75
Introduction

Squares on triangle sides

Objective. Interpret Pythagoras through areas of squares.

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

Learn: the key idea

Squares on triangle sides develops a connected mathematical idea rather than an isolated trick. Discover and apply the relationship between right-triangle sides. 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 equation is Pythagoras' theorem?

a² + b² = c²
Illustrated card showing a² + b² = c²
  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 a² + b² = c².

Answer: a² + b² = c²

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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

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