Question

PLZ HELP BEFORE I END MY LIFE-The sets of numbers 6, 8, 10 and 5, 12, 13 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples! ESSAY

Answer 1

Pythagorean Triples

Pythagorean TriplesA "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule

Example: The smallest Pythagorean Triple is 3, 4 and 5.

Example: The smallest Pythagorean Triple is 3, 4 and 5.Let's check it:

Example: The smallest Pythagorean Triple is 3, 4 and 5.Let's check it:32 + 42 = 52

9 + 16 = 25

9 + 16 = 25Yes, it is a Pythagorean Triplet

Triangles

TrianglesPythagoras

TrianglesPythagorasWhen a triangle's sides are a Pythagorean Triple it is a right angled triangle.

TrianglesPythagorasWhen a triangle's sides are a Pythagorean Triple it is a right angled triangle.pythagoras squares a^2 + b^2 = c^2

TrianglesPythagorasWhen a triangle's sides are a Pythagorean Triple it is a right angled triangle.pythagoras squares a^2 + b^2 = c^2See Pythagoras' Theorem for more details.

TrianglesPythagorasWhen a triangle's sides are a Pythagorean Triple it is a right angled triangle.pythagoras squares a^2 + b^2 = c^2See Pythagoras' Theorem for more details.Example: The Pythagorean Triple of 3, 4 and 5 makes a Right Angled Triangle:

TrianglesPythagorasWhen a triangle's sides are a Pythagorean Triple it is a right angled triangle.pythagoras squares a^2 + b^2 = c^2See Pythagoras' Theorem for more details.Example: The Pythagorean Triple of 3, 4 and 5 makes a Right Angled Triangle:triangle 3 4 5

Here are two more Pythagorean Triples:

Here are two more Pythagorean Triples:5, 12, 13 9, 40, 41

Here are two more Pythagorean Triples:5, 12, 13 9, 40, 41

Here are two more Pythagorean Triples:5, 12, 13 9, 40, 41 5, 12, 13 Triangle 9, 40, 41 Triangle

Here are two more Pythagorean Triples:5, 12, 13 9, 40, 41 5, 12, 13 Triangle 9, 40, 41 Triangle52 + 122 = 132 92 + 402 = 412

Here are two more Pythagorean Triples:5, 12, 13 9, 40, 41 5, 12, 13 Triangle 9, 40, 41 Triangle52 + 122 = 132 92 + 402 = 41225 + 144 = 169 (try it yourself)

Here are two more Pythagorean Triples:5, 12, 13 9, 40, 41 5, 12, 13 Triangle 9, 40, 41 Triangle52 + 122 = 132 92 + 402 = 41225 + 144 = 169 (try it yourself)

Here are two more Pythagorean Triples:5, 12, 13 9, 40, 41 5, 12, 13 Triangle 9, 40, 41 Triangle52 + 122 = 132 92 + 402 = 41225 + 144 = 169 (try it yourself) And each triangle has a right angle!

Here are two more Pythagorean Triples:5, 12, 13 9, 40, 41 5, 12, 13 Triangle 9, 40, 41 Triangle52 + 122 = 132 92 + 402 = 41225 + 144 = 169 (try it yourself) And each triangle has a right angle!(3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17)

Here are two more Pythagorean Triples:5, 12, 13 9, 40, 41 5, 12, 13 Triangle 9, 40, 41 Triangle52 + 122 = 132 92 + 402 = 41225 + 144 = 169 (try it yourself) And each triangle has a right angle!(3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17)(9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85)

Here are two more Pythagorean Triples:5, 12, 13 9, 40, 41 5, 12, 13 Triangle 9, 40, 41 Triangle52 + 122 = 132 92 + 402 = 41225 + 144 = 169 (try it yourself) And each triangle has a right angle!(3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17)(9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85)(15,112,113) (16, 63, 65) (17,144,145)

Example: scale 3, 4, 5 by 2 gives 6, 8, 10

Example: scale 3, 4, 5 by 2 gives 6, 8, 10Which also fits the formula a2 + b2 = c2:

Example: scale 3, 4, 5 by 2 gives 6, 8, 10Which also fits the formula a2 + b2 = c2:62 + 82 = 102

Example: scale 3, 4, 5 by 2 gives 6, 8, 10Which also fits the formula a2 + b2 = c2:62 + 82 = 10236 + 64 = 100

Plz mrk me as brainlist ✨