Pythagoras' Theorem

Learn how to use Pythagoras' Theorem, a2+b2=c2a^2 + b^2 = c^2, to find missing sides in right-angled triangles. Let's get started! 🚀

Pythagoras' Theorem - introduction visual

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Diagram explaining Pythagoras' theorem using two right-angled triangles, showing the equation a² + b² = c², and an example showing 3² + 4² = 5².Right-angled triangle with sides 5 cm, 13 cm, and unknown side x. Using Pythagoras' theorem, x is calculated as 12 cm with steps shown.Pythagoras' theorem example showing a right-angled triangle with sides 6, 8, and hypotenuse x. Equation 6² + 8² = x² solves for x = 10.3D Pythagoras theorem example in a cuboid: x² = 4² + 2² + 3², giving diagonal length x = √29.

🛎️ Pythagoras' Theorem

  • Only works in a right-angled triangle
  • The square of the hypotenuse equals the sum of the squares of the other two sides: a2+b2=c2a^2 + b^2 = c^2

🛎️ Finding a Missing Side in a Triangle

  • Identify the hypotenuse first (the side opposite the right angle)
  • Substitute the known lengths into a2+b2=c2a^2 + b^2 = c^2, then solve

🛎️ Finding the Distance Between Two Points

  • Draw a right-angled triangle using horizontal and vertical distances
  • Use Pythagoras to find the diagonal distance: d2=x2+y2d^2 = x^2 + y^2

🛎️ Using Pythagoras in 3D Shapes

  • Break the problem into two right-angled triangles
  • Apply Pythagoras twice to find the longest diagonal

Practice Questions

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