Pythagorean Theorem

FamiliesWhen working with right triangles, there are certain set of groups that you must know. There are three main sets that you must learn: a 3-4-5 triangle, 5-12-13 triangle and 7-24-25 triangle. The larger of the number of each set corresponds to the hypotenuse. Then the other two are part of each set correspond to the legs of the triangle.Another important note is that other groups of sets can be similar to the three basics ones presented here. For example a 3-4-5 is similar to a 6-8-10 triangle because of simplifying ratios between the two triangles. It is important for you to remember these basic families because if will save you time rather than doing a Pythagorean theorem to solve for each side if two sides are known.

Example45 45 90 ExampleIf x=4, what are the side lengths of a 45-45-90 degree triangle?

A.B.C.

45 45, 90Finally, a different special triangle is the 45-45-90 degree triangle. Each degree corresponds with its own leg. For instance the 45 degree angle corresponds with the two leg across from it which is x. And finally the 90 degree, right angle side, corresponds to the x square root of 2 leg (hypotenuse). Placing a value in for x will change the length of the sides of the triangles. For example if x=2, the length of the legs across from the 45 degrees is 2, and the hypotenuse is 2 square root of 2. Depending of the value of x, can change the lengths of the sides. The legs across the 45 degree are congruent because the legs and angles equal each other.

ExampleResourcesImage of 3,4,5 triangle on slide 1 is from: http://justcolleges.com/tests/triangles-tutorial-for-sat-gre-test-preparation/Image of 30-60-90 degree triangle on slide 1 is from: http://hotmath.com/hotmath_help/spanish/topics/30-60-90-triangles.htmlImage of 45-45-90 degree triangle on slide 1 is from: http://www.sparknotes.com/testprep/books/newsat/chapter20section4.rhtmlImage of 3,4,5 right triangle on slide 2 from: http://mathyear2013.blogspot.com/2013/08/another-rule-about-pythagorean-triples.htmlInformation from slides 2, 4, 6 is from: http://www.sparknotes.com/testprep/books/newsat/chapter20section4.rhtmlImages of 5-12-13 & 7-24-25 triangle is my own creation.Image of 30-60-90 degree triangle is my own creation.Image of 45-45-90 degree triangle is my own creation.Families Example

This triangle is similar to which basic family?A.B.C.

45 45 90 answerCorrect!

FeedbackMake sure you are simplifying as low as possibleFirst, choose two legs to work with.example: 15 & 36Second, make them into a fraction.example: 15/36Third, simplify the fraction.example:15/36=5/12

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30 60 90 example feedbackRemember that the leg across from the 30 is x, the leg across from the 60 is x square root of 3, and the leg across the 90, which is also the hypotenuse, is 2x

45 45 90 feedbackRemember that the leg across from the 45 is x, the leg across from the other 45 is x, and the leg across the 90, which is also the hypotenuse, is x square root of 2.

30 60 90 answerCorrect!

Families AnswerCorrect!

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