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Geometric Reasoning
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Note 1: Pythagoras's Theorem
In any right angled triangle, label the hypotenuse (longest side) c. Label the shorter sides a and b. To find the hypotenuse the formula is: c2 = a2 + b2 b a c
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To find one of the two shorter sides, rearrange the formula to:
a2 = c2 - b2 b a c
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x = 10 cm Example 1: Find x x 6cm 8cm Finding hypotenuse
Formula with + c2 = a2 + b2 8cm 6cm x x2 = x2 = 100 x = 100 x = 10 cm
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x = 12.104 cm Example 2: Find x x Shorter side Formula with - 12cm
a2 = c2 - b2 x2 = x2 = 145 x = 145 x = cm
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Page 215 Exercise K & L
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