Common Triples

In this video you will....

Look at common triples associated with the pythagoren theorem

How to use common triples to find a missing leg of a right triangle

Examples of common triples that are frequently seen in Geometry

Hi welcome to MooMooMath. Today we are going to look at common triples which are associated with the Pythagorean Theorem. Here is a common triple., a three, four,  five which works in the Pythagorean theorem because 3 squared ( 9 ) plus four squared ( 16 ) equals 5 squared ( 25  16 + 9 equals 25 ) so we have the numbers three. Four and five which are a common triple. In the Pythagorean Theorem. Below it is a triangle with a side of 6 and a hypotenuse of 10 and an X as the unknown side of X if you will notice this shows you a common triple. So three and 6 are associated with each other so they are corresponding sides and if I double 3 I get 6 and if I double 5 I get 10. Therefore if I double 4 I get 8 so the missing side is 8 so this is just applying the Pythagorean Theorem triple to an actual problem. So what are the actual rules for doing this? So what you will do is take your common triplets and multiple each number by the same factor. So we have a three, four, and five and in the example we multiplied each side by two to get a six, eight, ten triangle. You can also go back and multiple 3, 4, 5 by three and get 9, 12. and 15. You get do that with 4 10 or a 40, 50 right triangle. So what are the common triples? Let me show you several of the common triples you will see. 3, 4, 5 and multiples of those. A 5, 12, 13 is also a common triple. Because 5 squared plus 12 squared equals 13 squared. 25 plus 144 equals 169. Here are three more common triples 7, 24, 25 the 8, 15, 17 and the 20, 21, 29. So those are common triples you can take and multiple by sides by common factors. So you can see how this is done. Since I showed you the 3, 4, 5 triple first this time I will use the 5, 12, and 13. So if I were to make a table of possible values I will just draw the 5, 12, and 13 on top and make a list. If I multiple by two I get 10, 24, and 26. And multiple by three I get 15 26, 39 and by 4 I get 20 48 and 52 and those would be our common triples of 5, 12, 13. Hope this was helpful