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Using Pythagoras Theorem in Math Problems (Math Problem Sample)


State and prove Pythagoras theorem


Pythagoras Theorem
The theorem postulates that, to evaluate the hypotenuse, denoted d2, it is equal to the sum squares of the base and the height, denoted a2 + b2. The triangle is three sided with a perpendicular 900 angle. For the purpose of this report, we will use a as the height, b as the base and d as the hypotenuse, this is sufficient for the Pythagorean triple.
Suppose there exist a triangle as per the above assertion;
So that, a = The height, b = Base of the triangle and d = The hypotenuse of the triangle.
Using our introductory definition,
height2 + Base2 = Hypotenuse2
d2 = b2 + a2
Let’s us assume that a triangle ABD exist, and contains a structure with right angle triangle at B
We have to show that AD2 = AB2 + BD2
Mark a point H at the point between A and D and draw a perpendicular line to meet AD at H from BH
It is trivial that, △ABD ~ △ BHA
Therefore, ABAD = AHAB
Or, AB2 = AD × AH …………………………….……. (1)
This implies that △BHD ~ △ABD
Therefore, BCAD = CHBD
i.e.  BD2 = DH × HA ……………………………………. (2)

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