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Understanding Pythagoras' Theorem through Visuals

Pythagoras' theorem works on right-angled triangles by comparing areas of squares on sides. Learn how to find lengths and areas using this principle.

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Understanding Pythagoras' Theorem through Visuals

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  1. Pythagoras’ theorem only works on right – angled triangles If you draw squares on the two shorter sides… … and find their area. Area A Area B

  2. Area C Area A Area A + Area B = Area C The sum of their areas equals the area of the square on the longest side! Area B

  3. Find the length of x. Find the area of the smaller squares x 9cm2 3cm 4cm 16cm2

  4. x = 25 = 5cm Find the length of x. 25cm2 What will the length x be? x 9cm2 3cm add to find the area of the large square. 4cm 16cm2

  5. x = 100 = 10 Find the length of x. x x2 = 82 + 62 6cm x2 = 64 + 36 8cm x2 = 100

  6. x = 130 = 11.4 Find the length of x. x x2 = 92 + 72 7cm x2 = 81 + 49 9cm x2 = 130

  7. x = 80 = 8.9 Find the length of x. This time we need to find the area of one of the smaller squares … … so we need to subtract! 12cm x2 = 122 - 82 x x2 = 144 - 64 8cm x2 = 80

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