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Transcript
Geometry 7.4 454590 and 306090 Triangles Big Idea What is a 45-45-90 triangle? What is a 30-60-90 triangle? Why are they called "special" right triangles? How are the sides related to each other in a 45-45-90 triangle and a 30-60-90 triangle? How can we use these relationships to find missing side length? April 11, 2016 Agenda WarmUp 7.4 Special Right Triangles Investigation + Practice HW #7.4 Return quizzes WarmUp Simplify the following: 1 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 2 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 3 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 You now will be completing an investigation in your groups. Each group member has a different triangle but they all have a pattern between their sides. Your goal is to figure out this pattern. x 10 10 4 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 You now will be completing a second investigation in your groups. Each group member has a different triangle but they all have a pattern between their sides. Your goal is to figure out this pattern. Key Vocabulary (parts of a right triangle): short leg leg hypotenuse hypotenuse long leg leg 5 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 Big Idea - How are the sides of a 30-60-90 triangle related to each other? How can we use these patterns to find the lengths of missing sides? 6 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 12 12 x 6 6 7 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 Let's add these patterns to our theorem/postulate list... hypotenuse If then 454590 Triangle If short leg hypotenuse then long leg 306090 Triangle 8 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 9 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 10 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 11 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 12 Geometry 7.4 454590 and 306090 Triangles April 11, 2016 Exit Slip #7.4 - one paper per person. Do individually... 1) Find the value of x in each of the 454590 triangles below. Use the patterns of 454590 triangles and 306090 triangles rather than the Pythagorean Theorem 2) Find the values of x and y in each of the 306090 triangles below. #7.4 (PW)p.133: 112 (good practice) 454590 and 306090 Triangles or p.134: 1520 (challenge) 13