1 / 6

Families of Right Triangles

Families of Right Triangles. Lesson 9.6. Pythagorean Triples. Whole number combinations that satisfy the Pythagorean Theorem. (Uses multiples.) These triples can save you time and effort. How are these triangles related? These triangles are all members of the (3, 4, 5) family.

presta
Download Presentation

Families of Right Triangles

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. Families of Right Triangles Lesson 9.6

  2. Pythagorean Triples Whole number combinations that satisfy the Pythagorean Theorem. (Uses multiples.) These triples can save you time and effort. How are these triangles related? These triangles are all members of the (3, 4, 5) family. Not a triple because not whole numbers.

  3. Other common families: (5, 12, 13) which includes (15, 36, 39) as a member. (7, 24, 25) which includes (14, 48, 50) as a member. (8, 15, 17) which includes (4, 7.5, 8.5) as a member. There are infinitely many families, including (9, 40, 41), (11, 60, 61), (20, 21, 29), and (12, 35, 37), but most are not used very often.

  4. Principle of the Reduced Triangle Reduce the difficulty of the problem by multiplying or dividing the three lengths by the same number to obtain a similar, but simpler, triangle in the same family. Solve for the missing side of the easier triangle. Convert back to the original problem.

  5. Find the value of x. What do you notice about 55 and 77? The problem can be reduced by dividing each side by 11. 52 + y2 = 72 25 + y2 = 49 y2 = 24 y =

  6. Find AB Both methods get the same answer. Which method will you use? Method 1 (10, 24, ?) belongs to the (5, 12, 13) family. 10 = 5 • 2 24 = 12 • 2 So AB = 13 • 2 = 26 Method 2 102 + 242 = (AB)2 100 + 576 = (AB)2 676 = (AB)2 26 = AB

More Related