1. Lesson 8-7 The Pythagorean Theorem
Thee’uh-rem
(named after Pythagoras)

2. Building squares on right angles
Copy the image from the school text book and paste it on the slide or use sketchpad to create the same image in the book 2

3. Pythagorean theorem
In any right triangle, the sum of the squares of the lengths a and b of the legs is equal to the square of the length c of the hypotenuse.
Baseball diamond
Height of a building
Ramp of a moving truck
Measurement of TV
Two friends meeting at a particular destination 3

4. The Pythagorean Theorem
LESSON 8-7
Additional Examples
Find the length of the hypotenuse.
c2 = a2 + b2
Pythagorean Theorem
c2 =
Substitute.
c2 =
Simplify.
c2 = 841
Take the square root of each side.
c2 =
c = 29
The length of the hypotenuse is 29 in.
8-7

5. The Pythagorean Theorem
LESSON 8-7
Additional Examples
Find the missing leg of the triangle.
a2 + b2 = c2
Pythagorean Theorem
a = 252
Substitute.
a = 625
Simplify.
a – 225 = 625 – 225
Subtract 225 from both sides.
a2 = 400
Simplify.
a = 20
Take the square root of each side.
a2 =
The length of the leg is 20 ft.
8-7

6. 8.7: Applying the Pythagorean theorem6

7. Objective We use Pythagorean theorem to solve real-world situations
Sometimes, a triangle is not obvious but you can visualize the sides of a triangle and then draw a picture
Now, let’s work on a word problem.

8. The Pythagorean Theorem
LESSON 8-7
Additional Examples
A ladder, placed 4 ft from a wall, touches the wall 11.3 ft
above the ground. What is the approximate length of the ladder?
Draw a diagram to illustrate the problem.
c2 = a2 + b2
Use the Pythagorean Theorem.
c2 =
Substitute.
c2 =
c2 =
Square 4 and 11.3.
Add.
Use a calculator.
Take the square root of each side.
c =
c2 =
The length of the ladder is about 12 ft.
8-7

9. Homework Lesson 8-7 pp. 407-408 #s 1-10, 15-18, 22-24
(Can use a calculator if c2 is not a perfect square)
Complete Activity Lab if needed.