Converse of Pythagorean Theorem | MathHelp.com - By MathHelp.com
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| 00:0-1 | remember that the Pythagorean theorem states that if a triangle | |
| 00:05 | is a right triangle , then the sum of the | |
| 00:08 | squares of the legs of the triangle is equal to | |
| 00:12 | the square of the hypotenuse or a squared plus B | |
| 00:17 | squared equals c squared . The converse of the Pythagorean | |
| 00:22 | theorem , on the other hand , states that if | |
| 00:26 | the sum of the squares of two sides of a | |
| 00:28 | triangle is equal to the square of a third side | |
| 00:33 | , or a squared plus b squared equals c squared | |
| 00:38 | , then the triangle is a right triangle . Remember | |
| 00:43 | that the converse switches the order of the if and | |
| 00:48 | then statements . So in the pythagorean theorem problems , | |
| 00:53 | like the ones in the previous sections were given that | |
| 00:57 | a triangle is a right triangle , and we're asked | |
| 01:01 | to find the length of a missing side . In | |
| 01:05 | the converse of the Pythagorean theorem problems were given the | |
| 01:09 | lengths of all three sides of a triangle and were | |
| 01:13 | asked if we have a right triangle . So let's | |
| 01:17 | say we're given a triangle with sides of links 34 | |
| 01:22 | and five , and were asked to determine if it's | |
| 01:26 | a right triangle . The converse of the pythagorean theorem | |
| 01:31 | tells us that if we can show that a squared | |
| 01:34 | plus B squared equals c squared , then we'll know | |
| 01:39 | that it's a right triangle . So does three squared | |
| 01:45 | plus four squared equal five squared , Okay , three | |
| 01:54 | squared is nine , four squared is 16 And five | |
| 01:59 | squared is 25 . So we have nine plus 16 | |
| 02:06 | blank , 25 nine plus 16 is 25 . So | |
| 02:14 | we can see that 25 equals 25 . So a | |
| 02:20 | squared plus B squared equals c squared . And remember | |
| 02:26 | that if a squared plus B squared equals c squared | |
| 02:31 | , then the triangle is a right triangle . By | |
| 02:34 | the converse of the pythagorean theorem . So the triangle | |
| 02:39 | with sides of links 3 , 4 and five must | |
| 02:44 | be a right triangle . |
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