Learning Pythagoras theorem

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Presentation transcript:

Learning Pythagoras theorem

1. Pythagoras theorem ‘The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that knowledge of the theorem predates him. There is evidence that Babylonian mathematicians understood the formula, although there is little surviving evidence that they fitted it into a mathematical framework.’ http://en.wikipedia.org/wiki/Pythagorean_theorem

2. Algebraic equations Pythagoras is the use of a simple algebraic expression.

a2+b2=c2 3. pythagorean equation The number of the side times itself a2+b2=c2 The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c) Each letter (variable) represents a side

4. Right angled triangle This equation can only be used on a right angled triangle In a right angled triangle: the square of the hypotenuse is equal to the sum of the squares of the other two sides.

5. Breaking down the equation a2 = one length of the triangle b2 = another length of the triangle c2 = identified as the hypotenuse

6. Sides of a right-angled triangle HYPOTENUSE: The opposite side of the right angle in a right angled triangle, which is also the longest side. ADJACENT: Either of two sides having a common side and a common vertex. OPPOSITE: When two lines intersect, four angles are formed. The angles that are directly opposite to each other, can be vertically opposite angles and that are non-adjacent are the opposite angles.

7. Putting the equation into practice a2+b2=c2 x 72 + 42 = c2 7 x 7 = 49 4 x 4 = 16 49 + 16 = c2 Once the numbers have been squared, add a and b 49+16 = 65 65 = c2 Find the square root of both sides of the equation Square root of 65 = 8.06 Therefore c = 8.06 4 5