If you work through this section you should be able to:
The Pythagoras’ theorem relates to the lengths of the three sides of a right-angled triangle. The Pythagoras’ theorem states that the square on the longest side of a right-angled triangle is equal to the sum of the squares on the two shorter sides of the triangle.
The Pythagoras’ theorem can be used to find the length of the third side of the right-angled triangle if the lengths of the other two sides are provided. The Pythagoras’ theorem can also be used to determine whether a triangle has a right angle (90°).
The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
BC2 = AB2 +AC2
Given one side and the hypotenuse of a right-angled triangle as 5.6cm and 12.3cm respectively, find the length of the other side.
5.62 + x2 = 12.32
31.36 + x2 = 151.29
x2 = 119.93
x = 10.95cm
x2 = 52 + 72
x2 = 25 + 49
x2 = 74
x = 8.6cm
BC2 = 412 = 1681
AB2 + AC2 = 92 + 402 = 81 + 1600 = 1681
BC2 = AB2 + AC2
The triangle satisfies Pythagoras’ theorem and so is a right-angled triangle.You can download a version of this Pythagoras’ theorem activity in Word format:
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