7B Pythagorean Theorem and Its Converse

1. 7B Pythagorean Theorem and Its Converse OBJECTIVES: To determine missing measures using the Pythagorean Theorem To determine right triangles using the Converse of the Pythagorean Theorem

2. Right Triangle Parts Longest side Opposite rt. angle

3. NOTE: The Pythagorean Theorem is useful in finding missing lengths of sides in right triangles Right ∆  c2 = a2 + b2 hypotenuse leg leg

4. Using the Pythagorean Theorem EXAMPLE 1: Finding the Length of a Hypotenuse Given a right triangle with legs of lengths 5 cm and 12 cm, find the length of the hypotenuse.

5. Using the Pythagorean Theorem EXAMPLE 2: Finding the Length of a Leg Given a right triangle with hypotenuse of length 14 cm and leg of length 7 cm, find the length of the remaining leg.

6. Using the Pythagorean Theorem

7. NOTE: The Converse of the Pythagorean Theorem is useful in determining right triangles. c2 = a2 + b2 right triangle

8. The Pythagorean Theorem and Its Converse can be written as the following bi-conditional statement: Right ∆c2 = a2 + b2

9. Using the Converse of the Pythagorean Theorem: EXAMPLE 4: Determining Right Triangles 8 7 4√95 15 √113 36

11. EXAMPLE 5: Classifying Triangles • Determine if a triangle can be formed given the following lengths of sides. • If they can, classify the triangle as right, acute, or obtuse. a. 38 cm, 77cm, 86cm b. 10.5cm, 36.5cm, 37.5cm

12. To summarize: Pythagorean Theorem and Its Converse Right ∆  __________________ c2 =a2 + b2  ____________ Classifying Right Triangles c2 <a2 + b2  ____________ c2 >a2 + b2  ____________

13. Final Checks for Understanding • State the Pythagorean Theorem in your own words. • Which equations are true for ∆ PQR? Q r p P q R e. p2= q2 + r2

14. Final Checks for Understanding 3. State the Converse of the PythagoreanTheorem in your own words.

15. HOMEWORK ASSIGNMENT: Pythagorean Theorem and Its Converse WS, plus textbook:_______________________