1. 10.2(b) Notes: The Pythagorean Theorem and Its Converse
Date:
10.2(b) Notes: The Pythagorean Theorem and Its Converse
Lesson Objective: Use the Pythagorean Theorem to solve problems.
CCSS: G.SRT.8, G.MG.3
Real-Life App: How long of a ladder will we need? – DIGI #2
You will need: CPR, calculator

2. Lesson 1: Proving the Pythagorean Theorem
How or why does the Pythagorean Theorem work?
Leg Hypotenuse
a c
b Leg

3. Lesson 1: Proving the Pythagorean Theorem
Plot A(0, 3), B(4, 0) and C(0, 0). Connect the points to make a right triangle.

4. Lesson 1: Proving the Pythagorean Theorem
“Square” each leg and the hypotenuse. Find the area of each square.
Draw the squares in the 5x5 square. Then highlight the 4x4. There are 9 left over.

5. Lesson 1: Proving the Pythagorean Theorem
Because = 25, then a2 + b2 = c2.

6. Lesson 2: The Converse of the Pythago-rean Theorem
Pythagorean Converse:
If a2 + b2 = c2, then the Δ is a right Δ.

7. Lesson 2: The Converse of the Pythago-rean Theorem
Determine whether the measures can form a triangle. If so, determine if it is a right triangle.
11, 60, 61
2, 5, 6
3, 3, 4

8. Lesson 2: The Converse of the Pythago-rean Theorem
Determine whether the measures can form a triangle. If so, determine if it is a right triangle.
11, 60, 61

9. Lesson 2: The Converse of the Pythago-rean Theorem
Determine whether the measures can form a triangle. If so, determine if it is a right triangle.
B. 2, 3, 4

10. Lesson 2: The Converse of the Pythago-rean Theorem
Let’s find out what kind of triangle this is by constructing it with a compass or protractor.
2, 3, 4
30°
2” 3” ”
Move the board over to save this screen.

11. Lesson 2: The Converse of the Pythago-rean Theorem
Determine whether the measures can form a triangle. If so, determine if it is a right triangle.
3, 3, 4

12. Lesson 2: The Converse of the Pythago-rean Theorem
Let’s construct this one to find out what kind of triangle this is.
3, 3, 4
48°
3” ”
Compare this triangle to B. Have them find the new theorem.

13. Lesson 3: Pythagorean Inequality Theorem
If c2 > a2 + b2, then the Δ is an obtuse Δ.
If c2 < a2 + b2, then the Δ is an acute Δ.

14. Lesson 3: Pythagorean Inequality Theorem
Plot X(-7, -3), Y(-2, -5) and Z(-4, -1) on your coordinate plane. Determine if it is a right, acute or obtuse triangle.
Use Pythag. Thm to find side lengths.

15. 10.2: Do I Get It? Yes or No
Find the other leg of a right triangle in simplest radical form if one leg is 22 and the hypotenuse is 25.
Damon is locked out of his house and the only open window is on the second floor 12 feet above the ground. If a ladder needs to be placed 5 feet from the house, how long of a ladder does he need?

16. 10.2: Do I Get It? Continued
Determine whether the measures 7, 14, 16 can form a triangle. If so, determine if it is a right, acute or obtuse triangle.
Determine if ΔXYZ with vertices X(0,-6), Y(1, -5) and Z(3, -7) is an acute, right or obtuse triangle.

17. 10.2: Do I Get It? Continued
4. Determine if ΔXYZ with vertices X(0,-6), Y(1, -5) and Z(3, -7) is an acute, right or obtuse triangle.