Pythagorean Theorem
Published on Nov 19, 2015
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PRESENTATION OUTLINE
The Pythagorean theorem was created by Pythagoras of Samos. Pythagoras was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him
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The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The formula Is A^2+B^2=C^2
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EXAMPLE
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Proof: First of all, ΔABF = ΔAEC by SAS. This is because, AE = AB, AF = AC, and
∠BAF = ∠BAC + ∠CAF = ∠CAB + ∠BAE = ∠CAE.
ΔABF has base AF and the altitude from B equal to AC. Its area therefore equals half that of square on the side AC. On the other hand, ΔAEC has AE and the altitude from C equal to AM, where M is the point of intersection of AB with the line CL parallel to AE. Thus the area of ΔAEC equals half that of the rectangle AELM. Which says that the area AC² of the square on side AC equals the area of the rectangle AELM.
Similarly, the area BC² of the square on side BC equals that of rectangle BMLD. Finally, the two rectangles AELM and BMLD make up the square on the hypotenuse AB.
EXAMPLE PROBLEM 1
EXAMPLE PROBLEM 2
Real world application 1:
Let’s say two friends are meeting at a playground. One friend is located on the south-west corner of playground and other is located on the north-east corner of the playground. There are two ways to go let us see how you can take the help of Pythagoras' theorem to calculate the shortest distance between the meeting points of two friends. If you follow a road 3 miles east and then 4 miles north. Your total distance covered will be 3+4 = (7) miles but if you apply Pythagoras' theorem to calculate the distance you will get:
5 miles=C
So this will save them 2 miles distance.
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Real world problem 2:
Painters use ladders to paint on high buildings and often use the help of Pythagoras' theorem to complete their work. Take for example a painter who has to paint a wall which is about 8 m high. The painter has to put the ladder 6 m away to avoid a rack in between. What will be the length of the ladder required by the painter to complete his work? You can calculate it using Pythagoras' theorem:
10m =C
Thus, the painter will need a ladder 10 meters high.
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