Pythagorean Theorem Lesson

1. Introduction Introduction

2. The Pythagorean Theorem

3. Upon completing this lesson you will be able to: Identify sides of Right Triangle as either Legs or Hypotenuse Explain the Pythagorean Theorem Apply Pythagorean Theorem to find length of the sides of Right Triangles

4. Recall: TrianglesClassified In Two Ways Size of Angle Acute-All Angles less than 90 degrees Obtuse-One Angle Over 90 degrees Right-One 90 degree angle Length of Sides Equilateral-All three sides equal in length Isosceles-Two sides of equal length Scalene-No sides of equal length

5. Right Triangle LEG HYPOTENUSE LEG 90°

6. Pythagorean Theorem a2 + b2 = c2 HYPOTENUSE LEG c a b LEG

7. Pythagorean Theorem Legs - Two sides (a and b) that form the right angle Hypotenuse - Side opposite the right angle; called c Formula a2 + b2 = c2

8. Apply Theorem a=3 C=? b=4 a² + b² = c² 3²+ 4²= c² 9 + 16 = c² 25 = c² c = 5

9. More Practice 4² + 5² = C² a2 + b2 = c2 16 + 25 = C² C=? 41 = C² A=4 √41 = C B=5 3² + 6² = C² 9 + 36 = C² C=? 45 = C² B=3 √45 = C A=6

10. Evaluation Identify the sides of each triangle as either legs or hypotenuse (assume all shapes are right triangles)

11. Evaluation Complete the five equations with a partner (assume all shapes are right triangles and Show Your Work) 1) 2) 3) 4) 5) c=? c=? a=4 a=2 a=6 c=? b=5 b=7 b=3 c=? a=1 c=? a=4 b=9 b=8