1. Special Right Triangles

2. Right triangles have one 90 o angle The longest side is called the HYPOTENUSE It is directly across from the 90 o The other sides are called LEGS Hypotenuse LEG

3. Pythagorean Theorem The sides of a right triangle satisfy this theorem: a 2 + b 2 = c 2 LEG Hypotenuse

4. Pythagorean Theorem Review

5. Pythagorean Theorem Practice

6. Converse of the Pythagorean Theorem

7. Converse of Pythagorean Theorem

8. Solutions:

9. Pythagorean Triples A Pythagorean triple is a set of nonzero whole numbers a,b and c that satistify the Pythagorean theorem. 3,4,5 5,12,13 8,15,17 7,24,25

10. Practice IXL - Pythagorean Inequality Theorems

11. Special Right Triangle Investigation: 45-45-90 Draw an isosceles right triangle with legs that measure 4 cm. Use the Pythagorean Theorem to find the length of the hypotenuse. Leave answer in simplest radical form. Repeat the steps above for an isosceles right triangle with legs that measure 12 cm. Now draw an isosceles right triangle with a hypotenuse that measures 7 cm. Use the Pythagorean Theorem to find the length of the congruent legs. Leave your answer in simplest radical form.

12. Special Right Triangle Investigation: 30-60-90 Draw an equilateral triangle with side lengths of 6 cm. Draw the perpendicular bisector from the top vertex. Label the angle measures. Use the Pythagorean Theorem to find the height of the triangle. Leave answer in simplest radical form. Repeat the steps above for an equilateral triangle with side lengths of 10 cm.

13. 45 °- 45°- 90° In a 45 ° - 45° - 90° triangle, both legs are congruent and the length of the hypotenuse is the square root of 2 times the length of the leg.

14. 30 ° - 60° - 90°

17. Ex. Find the values of the variable. 1. 2. 3 3 x x x 3. 4. x

18. Ex. Find the values of the variable(s). 1. 2. 30 60 6 s 5 t s 30 60

19. Videos 45-45-90 Triangles 30-60-90 Triangles

20. Practice Khan Academy Kuta Software IXL