3.1 Pythagorean Relationship

• Sides of a right-angled triangle: base, height and hypotenuse
• Pythagorean relationship: the square on the hypotenuse equals the sum of the squares on the other two sides
• The 3-4-5 triangle and other right-angled triangles
• Applying Pythagoras Theorem to find a missing side
• Real-life uses: ladders, roofs, staircases, rectangular plots and safety

• recognise the sides of a right-angled triangle in different situations
• identify Pythagorean relationships in different situations
• apply Pythagorean relationship to real-life situations
• promote the use of Pythagoras Theorem in real-life situations

“How do we use Pythagorean relationships in real-life situations?”

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1. Sides of a right-angled triangle
   40 min · 1 practice tasks · quiz
   Name base, height and hypotenuse on a right-angled triangle, including a ladder leaning on a wall.
2. The Pythagorean relationship
   40 min · 1 practice tasks · quiz
   Count squares on a 3-4-5 triangle and state that the square on the hypotenuse equals the sum of the squares on the other two sides.
3. Finding the hypotenuse
   40 min · 1 practice tasks · quiz
   Use a² + b² = c² to calculate the longest side when the two legs are known.
4. Pythagoras in real life
   40 min · 1 practice tasks · quiz
   Find a missing leg, then apply the theorem to ladders, roofs, plot diagonals and safety.