Please help! am so lost.

Question

1. Use the m & n method to create your own Pythagorean Triple
2. Draw and label a Right Triangle with the Pythagorean Triple you created
3. Use the Pythagorean Theorem to prove that your Pythagorean Triple is valid

Answer 1

You get to pick two random values of m and n (but pick m bigger than n), for instance m = 6 and n = 5. Now, use the following rules to generate the sides of you right triangle:

a = m² − n²

1. In this case, that makes a = 6² - 5² = 36 - 25 = 11

b = 2mn

1. In this case, that makes b = 2•6•5 = 60

c = m² + n²

1. In this case, that makes c = 6² + 5² = 36 + 25 = 61

So this is your "Pythagorean Triple" (a, b, c) = (11, 60, 61) or here is a sketch of your triangle:

As a check, try the Pythagorean Theorem: a² + b² = c² and you will see it works.

Answer 2

a, b - lengths of legs of the right triangle

c - length of hypotenuse

The "n" and "m" method of making Pythagorean triples:

For "n" and "m", any two positive integers, such that m > n,

a = m² - n²

b = 2mn

c = m² + n²

Calculating Pythagorean triple:

for m = 2, n =1,

a = 4 - 1 = 3

b = 2•2•1 = 4

c = 4 + 1 = 5

Therefore, 3, 4 and 5 are Pythagorean triple.

Checking:

9 +16 = 25 ← Pythagorean theorem

25 = 25 → checks out!

Answer 3

Pick two natural numbers m and n with gcd(m, n) = 1

Your triple is three numbers representing the sides of the triangle.

2mn and |m² - n²| are the sides of the triangle and m² + n² is your hypotenuse.

For example. Suppose the numbers you choose are m = 2 and n = 1

2(2)(1) and |(2)² - (1)²| are the sides and (2)² + (1)² is the hypotenuse.

Therefore 4 and 3 are the sides and 5 is the hypotenuse and your triple is 3-4-5.