{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

SampleWritingAssignment

# SampleWritingAssignment - For example 3 4 5 6 8 10(times 2...

This preview shows pages 1–2. Sign up to view the full content.

Sample Writing Assignment: Pythagorean Theorem by Gwen Fisher Write about the Pythagorean Theorem. First, we start with a statement of the theorem: Let ABC be a right triangle with sides of lengths a , b , and c . Let the sides with lengths a and b be the legs, and let c be the hypotenuse. Then a ^2 + b ^2 = c ^2. Also, if a ^2 + b ^2 = c ^2, then ABC is a right triangle. c A a b C B An illustration of the theorem is shown with the picture below. c A a b C B The theorem tells us that if the angle at C is a right angle then the sum of the areas of the squares with sides a and b is equal to the area of the square with sides c . We can give some examples of the theorem. 3^2 + 4^2 = 5^2, so a square with sides of length 3, 4, and 5 is a right triangle. Similarly 5, 12, 13 is the side lengths of a right triangle. These sets of numbers are called Pythagorean Triples. Also, all multiples of Pythagorean Triples are Pythagorean triples.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: For example, 3, 4, 5 6, 8, 10 (times 2) 9, 12, 15 (times 3) 1.5, 2, 2.5 (times 0.5) These are all Pythagorean Triples. Let’s see what happens if we have a triangle that is not a right triangle. I know that equilateral triangles are not right. So if I take a triangle with sides all 1 and I try to use the Pythagorean Theorem, I get 1^2 + 1^2 = 1^2 or 2 = 1, which is nonsense. So I have shown that if a triangle does not have a right angle, then we do not always get a ^2 + b ^2 = c ^2. If I know any two sides of a right triangle, then I can always find the third. Let’s see what happens if we fix a = 1 b x 0 1 2 3 4 5 6 7 8 c √ ( x ^2 + 1) 1 √ 2 √ 3 2 √ 5 √ 6 √ 7 √ 8 3 So if a = 1, then we can think of c as a function of b , namely c is f ( x ) = √ ( x ^2 + 1). b or x c or f ( x ) (Note that this is about 350 words.)...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

SampleWritingAssignment - For example 3 4 5 6 8 10(times 2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online