1. Unit 6 Lesson 1 The Pythagorean Theorem
CCSS
Lesson Goals
G-SRT 4: Prove theorems about triangles.
Use the Pythagorean Th. to find missing side lengths in a right triangle.
Recognize a Pythagorean Triple.
ESLRs: Becoming Effective Communicators,
Competent Learners and Complex Thinkers

2. the Pythagorean Theorem
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. c a b

3. proof Given Perpendicular Post. Right D Altitude ThB e D c a f A C b
Statement
Reason
Given
Perpendicular Post.
Right D Altitude Th
Def similar polygons
Cross-Products Prop.
Add. Prop. of =
Distributive Prop
Segment Add. Post
Substitution

4. definition A set of three positive integers: a, b, c
Pythagorean Triples
A set of three positive integers: a, b, c
that satisfy the equation
Examples
3, 4, and 5
5, 12, and 13
8, 15, and 17

5. example Find the missing sideB a A C 12
Do the side lengths form a Pythagorean Triple?

6. You Try Find the missing sideB c 7 A 24 C
Do the side lengths form a Pythagorean Triple?

7. You Try Find the missing side
Do the side lengths form a Pythagorean Triple?

8. example
Find the area of the triangle.

9. You Try
Find the area of the triangle

10. example Two antennas are each supported by 100 foot cables.
If the cables are attached to the antennas 50 feet from
the ground, how far apart are the antennas? d
50 ft
100 ft
100 ft
50 ft x

11. summary How is the Pythagorean Theorem useful?
What is the difference between the Pythagorean Theorem in general and a Pythagorean Triple?

12. Today’s Assignment
p. 538: 8, 14, 18 – 28 e, 31 – 33, 37

13. Find the unknown side length. Simplify answers that are radicals
Find the unknown side length. Simplify answers that are radicals. Tell whether the side lengths form a Pythagorean triple.
Find the area of the figure. Round decimal answers to the nearest tenth.
Find the value of x. Simplify answers that are radicals.
The variables r and s represent the lengths of the legs of a right triangle, and t represents the length of the hypotenuse. The values of r, s, and t form a Pythagorean triple. Find the unknown value.