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

State and prove Pythagoras theorem

source..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

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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