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# Using Pythagoras Theorem in Math Problems (Math Problem Sample)

Instructions:

State and prove Pythagoras theorem

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Content:

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
Proof
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
Or, AB2 = AD × AH …………………………….……. (1)
This implies that △BHD ~ △ABD
i.e.  BD2 = DH × HA ……………………………………. (2)

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