1 / 11

Pythagorean Triples

Pythagorean Triples. Fact. In a right triangle, the sides touching the right angle are called legs. The side opposite the right angle is the hypotenuse . The Pythagorean Theorem ,. a 2 + b 2 = c 2 , relates the sides of RIGHT triangles.

fonda
Download Presentation

Pythagorean Triples

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Pythagorean Triples

  2. Fact In a right triangle, the sides touching the right angle are called legs. The side opposite the right angle is the hypotenuse.

  3. The Pythagorean Theorem, a2 + b2 = c2, relates the sides of RIGHT triangles. a and b are the lengths of the legs and c is the length of the hypotenuse.

  4. A Pythagorean Triple… • Is a set of three whole numbers that satisfy the Pythagorean Theorem. • What numbers can you think of that would be a Pythagorean Triple? • Remember, it has to satisfy the equation a2 + b2 = c2.

  5. Pythagorean Triple: • The set {3, 4, 5} is a Pythagorean Triple. • a2 + b2 = c2 • 32 + 42 = 52 • 9 + 16 = 25 • 25 = 25

  6. Show that {5, 12, 13} is a Pythagorean triple. • Always use the largest value as c in the Pythagorean Theorem. • a2 + b2 = c2 • 52+ 122= 132 • 25 + 144 = 169 • 169 = 169

  7. Show that {2, 2, 5} is not a Pythagorean triple. • a2 + b2 = c2 • 22+ 22= 52 • 4 + 4 = 25 • 8 ≠ 25 • Showing that three numbers are a Pythagorean triple proves that the triangle with these side lengths will be a right triangle.

  8. How to find more Pythagorean Triples • If we multiply each element of the Pythagorean triple, such as {3, 4, 5} by another integer, like 2, the result is another Pythagorean triple {6, 8, 10}. • a2 + b2 = c2 • 62+ 82= 102 • 36 + 64 = 100 • 100 = 100

  9. By knowing Pythagorean triples, you can quickly solve for a missing side of certain right triangles. • Find the length of side b in the right triangle below. • Use the Pythagorean triple {5, 12, 13}. • The length of side b is 5 units.

  10. Find the length of side a in the right triangle below. • It is not obvious which Pythagoreantriple these sides represent. • Begin by dividing the given sides by their GCF (greatest common factor) • { ___, 16, 20} ÷ 4 • { ___, 4, 5} • We see this is a {3, 4, 5} Pythagorean triple. • Since we divided by 4, we must now do the opposite and multiple by 4. • {3, 4, 5} • 4 = {12, 16, 20} • Side a is 12 units long.

More Related