The Pythagorean Theorem

8th Grade Pre-AlgebraPythagorean Theorem PPT

Molly Thompson

Pythagoras

•Born about 569 BC in Samos, Ionia•Died around 475 BC•Son of a merchant

•Greek mathematician•Described as the first pure mathematician•Introduced to mathematics by philosophers of his time•Interested in the principles, concepts, and proofs of mathematics

•The first mathematician to prove what is now known as The Pythagorean Theorem

The Pythagorean Theorem• The Pythagorean Theorem is a formula that one uses to find the length of a

side of a right triangle.

• Although Pythagoras first proved the Pythagorean Theorem, the idea is linked to the early Babylonians.

• History is that Pythagoras studied with men known as “rope stretchers,” who were men that built pyramids. The Pythagorean theorem was discovered through the ropes that were used to calculate lengths needed to build pyramids in order to lay their foundations accurately.

• Originally Pythagoras thought the Pythagorean Theorem was based solely on triples but later through the discovery of irrational numbers, found that it just had to satisfy the equation a2 + b2 = c2.

The Pythagorean Theorem

The Pythagorean Theorem states:

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

A right triangle is made of up 3 legs. The two that form the right angle are a and b, and the leg across from the right angle is called the hypotenuse, c.

Examples of The Pythagorean Theorem

• Find a: Find c: a2 + b2 = c2 a2 + b2 = c2

a2 + 82 = 102 52 + 122 = c2

a2 + 64 = 100 25 + 144 = c2

- 64 - 64 c2 = 169 a2 = 36 c = 13 a = 6

a

8

10c

12

5

Applications of The Pythagorean Theorem

The Pythagorean Theorem can be used for…– Finding the length of a ball thrown on a baseball field

– Finding the length of a ladder or the height of a building

– Finding the distance between two people or places

– Finding the length of a ramp

– Finding the measurement of a TV (a tvs size is determined

by measuring its diagonal)

Real-life Pythagorean Theorem Problems

To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?

a2 + b2 = c2

342 + 412 = c2

1156 + 1681 = c2

2837 = c2

c = 53.3 meters

Since you would walk about 53 meters if you went through the pond and 75 meters if you walked around, you would save 22 meters if you could travel through the pond.