6.1 Pythagoras’ Theorem


6.1 Pythagoras’ Theorem

6.1.1 Pythagoras’ Theorem
1. In a right-angled triangle, the hypotenuse is the longest side of the triangle.
2. Pythagoras’ Theorem:

  In a right-angled triangle, the square
  of the hypotenuse is equal to the sum
  of the squares of the other two sides.
Example 1:
 
Solution:
x 2 = 5 2 + 12 2 = 25 + 144 x = 169 = 13  

Example 2:
 
Solution:
x 2 = 15 2 9 2 = 225 81 x = 144 = 12

3. Pythagorean triples
are three whole numbers that form the sides of a right-angled triangle.

Example:
(a) 3, 4, 5
(b) 6, 8, 10
(c) 5, 12, 13
(d) 8, 15, 17
(e) 9, 12, 15


6.1.2 The Converse of the Pythagoras’ Theorem
 
 
  In a triangle, if the sum of the squares of the two sides
  is equal to the square of the longest side, then the angle
  opposite the longest side is a right angle.

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