7-3 Special Right Triangles

1. 7-3 Special Right Triangles Honors Geometry April 8, 2013

2. Warm Up • State if the triangle is acute, right or obtuse • Is it possible to have an isosceles right triangle?

3. Agenda • Warm Up • Homework Check • Discovery Activity – Special Right Triangles • 7-3 Special Right Triangles Notes • Examples • Homework

4. Homework Check • SOLUTIONS

5. Discovery Activity • Organize desks into your groups • As a group, read through the worksheet and answer all questions • You will be using your prior knowledge to answer questions and discover patterns • Always attempt to do the problems and try new things with your group before asking for assistance • When you are finished, report your findings to Mr. K

6. 7-3 Special Right Triangles 45-45-90 • If the measures of the angles of a triangle are 45, 45, and 90, then the triangle is an isosceles right triangle

7. 45-45-90 Triangle • What pattern did you notice while working with 45-45-90 Triangles? • The legs of a 45-45-90 Triangle are congruent and the hypotenuse is times as long as a leg

8. Example 1 • Find the value of x and y

9. Example 2 • Find the value of x and y

10. 30-60-90 Triangles • In a 30-60-90 Triangle we have a short leg, long leg, and hypotenuse Hypotenuse Long Leg Short Leg

11. 30-60-90 Triangles • How can we find the lengths of the sides of a 30-60-90 Triangle? • If we use reflection, what type of triangle do we have? • Equilateral • The value of m must be…? • 2 • Now we can work backwards to find n • n=

12. 30-60-90 Triangles • What pattern do we have with 30-60-90 Triangles? • In a 30o-60o-90o Triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg

13. Example 3 • Find the value of x and y

14. Example 4 • Find the value of x and y

15. Classwork • Complete Evens or Odds from worksheet

16. Homework • Complete worksheet