Pythagoras lived in the 500's BC,

1
Pythagoras lived in the 500's BC, and was one of
the first Greek mathematical thinkers. He had a
group of followers known as the Pythagoreans who
followed him around and taught other people what
he had taught them.
Source http//www.historyforkids.org/learn/greeks
/science/math/pythagoras.htm
2
Pythagoreans were interested in philosophy, but
especially in music and mathematics, two ways
of making order out of chaos. Music is noise
that makes sense, and mathematics is rules for
how the world works.
Source http//www.historyforkids.org/learn/greeks
/science/math/pythagoras.htm
3
Pythagoras himself is best known for proving
that the Pythagorean Theorem was true.
Source http//www.historyforkids.org/learn/greeks
/science/math/pythagoras.htm
4
The Pythagorean Theorem says that in a right
triangle, the sum of the squares of the two
right-angle sides will always be the same as the
square of the hypotenuse (the long side). A2
B2 C2.
Source http//www.historyforkids.org/learn/greeks
/science/math/pythagoras.htm
5
A Tale of Three Cities The Pythagorean Theorem
Step-by-Step Instructions

• Using Google Maps, find three cities that form a
  right triangle. Left-click and hold the mouse to
  move the map to any location on the planet. Zoom
  in and out until the three cities fill the map
  window.
• Print the map to a printer or print to a PDF
  creator program. Many of these programs are
  available for free. If you are using the PDF
  method, instead of saving the map as a PDF, use
  the PDF creator software to save the map as a
  JPEG (photo). Save it into a specific folder.
  Next, in that folder right-click on the map
  photo, choose copy and then open a new
  Presentation document where you will paste the
  map onto a slide.
• On the printed map, use a straight edge to draw a
  right triangle between the three cities. If you
  are using the PDF/JPEG method, use your
  Presentation software to open and paste a right
  triangle on top of the JPEG map. You can edit
  the triangle using the Format Shape function
  (remove the fill, the thicken the line, change
  the line color, etc.)
• On a separate slide, insert a Right Triangle,
  then add labels for the three sides and the three
  City Names.
• On another slide, write out the definition for
  the Pythagorean Theorem (see example).
• On the same slide, use a Distance Finder
  website to find the actual distance between the
  cities on side a. and the cities on side b. of
  the Right Triangle (see example).
• Use the Pythagorean Theorem to solve for the
  distance of side c (see example).
• On this same slide, give the name of side c.
• Next, solve the following problem. Traveling at
  an average rate of 50 miles per hour, calculate
  how long it will take to make a round trip
  journey to all three cities, including an 8-hour
  sight-seeing tour in each city. Show this on a
  separate slide.
• 10. Using Custom Animation in Microsoft
  Powerpoint, create a presentation in which you
  move a vehicle around to each city on your map.
  Choose a vehicle using Clip Art or a photo.
• 11. As your vehicle reaches each city, stop and
  present 10 facts about that city (see list
  provided). Show these facts on a separate slide
  for each city.

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A Tale of Three Cities The Pythagorean Theorem
The first step is to go to Google Maps and use
the Zoom tool to zoom in and out until you find
three cities that form a right triangle.
City 1
City 3
City 2
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A Tale of Three Cities The Pythagorean Theorem
A Right Triangle placed on top of a JPEG photo
of a Google Map.
Students may print the Google map to a printer
and use a ruler to draw a right triangle on the
map or print the map to a PDF creator program and
save it as a JPEG photo. If the PDF method is
used, students can copy the map into the
presentation software and then insert a right
triangle on top of the map as shown here using
the Insert gt Basic Shapes command.
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A Tale of Three Cities The Pythagorean Theorem
City Name 1
Students must draw a right triangle in the
presentation software with labels for the cities
and the sides of the triangle.
City Name 3
City Name 2
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A Tale of Three Cities The Pythagorean Theorem
San Angelo
Example
Galveston
Dallas
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A Tale of Three Cities The Pythagorean Theorem
The equation for the
Pythagorean Theorem is _____________________
Example
Use a Distance Finder website to find The
distance between City 1 and City 2 (Side a.)
___________ miles. The distance between City 2
and City 3 (Side b.) ___________
miles. Using the equation for the Pythagorean
Theorem, solve for the distance between City 1
and City 3 (Side c.). 232 miles2 269 miles 2
c2 53,824 72,361 c2
126,185 c2



The distance between City
1 and City 3 ____________ miles. Side c is
called the _______________________
232
269
c _______ miles
355
355
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A Tale of Three Cities The Pythagorean Theorem
In our example, the total distance is 232 miles
269 miles 355 miles 856 miles
A nice little getaway.
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A Tale of Three Cities The Pythagorean Theorem
Solve this problem.
You will make a round trip journey to all three
cities traveling at an average rate of 50 miles
per hour. Additionally, you will stay 8 hours in
each city on sightseeing tours. How long will
the trip take? _________ hours.
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If we know the distance (miles) and the rate
(miles per hour), we can find the time (hours)
based on the following formula
Distance Rate x Time d r x t
856 miles 50 miles per hour x t
t 17 hours, then add 24 hours 41 hours
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A Tale of Three Cities The Pythagorean Theorem
Using clip art or a photo, insert a vehicle onto
your map. Move it around to all three cities
using Custom Animation. Stop the animation after
each leg of your trip, and go to the facts for
that city.
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A Tale of Three Cities The Pythagorean Theorem

• FACT SHEET
• City Name
• State
• Year Founded
• Current Population
• Longitude and Latitude
• Weather Fact
• Current Mayor
• Form of Government
• Largest Employer
• Two Colleges
• A fun activity that you would do if you were
  there.

Find these 10 facts on each city.
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Click your mouse or hit the space bar to move the
car along its trip.
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San Angelo

• Texas
• 1867
• 88,439
• 3127'11"N / 10027'9"W
• San Angelo averages 251 days of sunshine a year
• Alvin New
• Council-manager
• Shannon Medical Center
• Angelo State University and Howard College
• 10 miles of river frontage on the Concho River
• winding through downtown and beyond.

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Dallas

• Texas
• 1841
• 1,279,910
• 3247'0"N / 9648'0"W
• Winters in Dallas are generally mild, with
• normal daytime highs ranging from
• 55 F (13 C) to 70 F (21 C)
• Tom Leppert
• Council-manager
• American Airlines (22,077 employees)
• Southern Methodist University (SMU) and Texas
  Womans University
• Dallas Cowboys in the new Cowboys Stadium

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Galveston

• Texas
• The first permanent European
• settlements on the island were
• constructed around 1816 by the
• pirate Louis-Michel Aury
• 57,466
• 2918'04"N / 9447'51"W
• In 1900, the island was struck by a devastating
  hurricane. It holds the record as the United
  States' deadliest natural disaster killing 6,000
  to 8,000 people on the island
• Lyda Ann Thomas
• Council-manager
• University of Texas Medical Brach at Galveston
• Galveston College and Texas AM University at
  Galveston
• Mardi Gras, Moody Gardens

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Wow, that was a fun trip.
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The End. I hope you enjoyed this lesson.