The Pythagorean Theorem

Warm Up:Tell a neighbor

which sides of the triangle are the legs and which side is the hypotenuse.

So what is the Py-tha-go-re-an Theorem?

You will discover the theorem later.You will discover the theorem later. The theorem deals with right triangles The theorem deals with right triangles

and how their sides relate to each and how their sides relate to each other. other.

Used:Used: To find a missing side in a right To find a missing side in a right

triangle.triangle.To prove a triangle is a right To prove a triangle is a right

triangle.triangle.

History Lesson! Pythagoras was born around Pythagoras was born around

590 B.C. 590 B.C. Greek mathematicianGreek mathematician Earlier people knew the Earlier people knew the

theorem, however, theorem, however, Pythagoras was formally Pythagoras was formally credited. credited.

Discover the Theorem Yourself!Draw one leg of the Draw one leg of the

triangle with a length of 4 triangle with a length of 4 units down.units down.

Draw the other leg of the Draw the other leg of the triangle with a length of 3 triangle with a length of 3 units across.units across.

Connect the two ends. Connect the two ends. This side is 5 units long.This side is 5 units long.

YouYou’’ve formed a right ve formed a right triangle!triangle!

3

45

Discover the Theorem Yourself…Discover the Theorem Yourself… Extend the 4 unit leg to Extend the 4 unit leg to

the left to create a the left to create a square.square.

Extend 3 unit leg down Extend 3 unit leg down to create a square.to create a square.

Repeat with the 5 unit Repeat with the 5 unit length.length.

Find the area of each Find the area of each square.square.

How do they relate to How do they relate to each other?each other?

Thus…Thus…a² + b² = c²a² + b² = c²

Video http://www.youtube.com/watch?

v=uaj0XcLtN5c&feature=related

Pythagorean TriplesConsist of three positive integers a, b, and c, such Consist of three positive integers a, b, and c, such

that: that:

Examples: Examples: 3, 4, 53, 4, 5

6, 8,106, 8,10

5, 12, 135, 12, 13

222 cba 222 543

Video

Is it a right triangle?Is it a right triangle?

10, 25, 2610, 25, 26Does 10² + 25² = 26² ?Does 10² + 25² = 26² ?

NONO 6, 8, 106, 8, 10

Does 6² + 8² = 10² ?Does 6² + 8² = 10² ?YESYES

Your turn…

Let’s play Pythagorean Let’s play Pythagorean Memory!Memory!

Compared to all possible groups Compared to all possible groups of 3 numbers, how many do you of 3 numbers, how many do you

think will be Pythagorean Triples?think will be Pythagorean Triples?

Puzzle Activity

Video

3/4/15: Pick 3/4/15: Pick ONEONE. Show work!. Show work!

1.1. If a = 7 and b = 24, what is c?If a = 7 and b = 24, what is c?

2525

2.2. If a = 20 and c = 29, what is b?If a = 20 and c = 29, what is b?

2121

HW check today!

More Pythagorean TheoremEQ: How is a missing side of a right triangle found?

A funny for you…

Think-Pair-ShareThink-Pair-Share

1.1. How do you remember directions How do you remember directions like north, south, east, and west?like north, south, east, and west?

2.2. How could a map be used to How could a map be used to make amake a““right triangleright triangle””??

3.3. How could a ladder be used to How could a ladder be used to make amake a““right triangle”?right triangle”?

Spanville is 40 miles north of Mechanicsburg, and Franktown is 120 miles east of Spanville.

Spanville

How far is a direct drive from Franktown to Mechanicsburg?

Example 1

WS Problem #1WS Problem #1To get from point A to To get from point A to point B you must avoid point B you must avoid

walking through a pond.  walking through a pond.  To avoid the pond, you To avoid the pond, you must walk 34 meters must walk 34 meters south and 41 meters south and 41 meters east.  To the nearest east.  To the nearest

meter, how many meters meter, how many meters would be saved if it were would be saved if it were possible to walk through possible to walk through

the pond?  the pond? 

You just picked up a ground ball at 1st base, and you see the other team's player running towards 3rd base. How far do you have to throw the ball to get it from 1st base to 3rd base to throw the runner out?

90 feet90 feet

WS Problem #2

Example 3Example 3 Mr. Rattay wants to put in an underground sprinkler system at EMMS. A drawing of the system is shown. About how many total feet of water pipe will MMS need to buy?

If piping costs $5.00 per foot, how much is the total coast?

Video Links Jeopardy Game:

http://www.math-play.com/Pythagorean-Theorem-Jeopardy/Pythagorean-Theorem-Jeopardy.html

 Rap: http://www.youtube.com/watch?v=DRRVu-RHQWE&feature=related

 Football: http://nbclearn.com/nfl/cuecard/51220 Cowboy’s coach: http://nesn.com/2013/07/jason-

garrett-says-its-important-for-football-players-to-understand-pythagorean-theorem-video/