6-3 Pythagorean Theorem - Mrs. Spanier`s Awesome Math Site

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Transcript 6-3 Pythagorean Theorem - Mrs. Spanier`s Awesome Math Site

A funny for you…
6-3 Pythagorean Theorem
Mrs. Spanier
So what is the Py-tha-go-re-an
 You will discover the theorem later.
 The theorem deals with right triangles
and how their sides relate to each
 Used:
 To find a missing side in a right
To prove a triangle is a right triangle.
History Lesson!
 Pythagoras was born around
590 B.C.
 Greek mathematician
 Earlier people knew the theorem,
however, Pythagoras was
formally credited.
You may be wondering…
 How did people who lived in
the B.C. era create right
 Using rope!
Discover the Theorem Yourself!
 Draw one leg of the
triangle with a length of 4
units down.
 Draw the other leg of the
triangle with a length of 3
units across.
 Connect the two ends.
This side is 5 units long.
 You’ve formed a right
Discover the Theorem Yourself…
 Extend the 4 unit leg to
the left to create a
 Extend 3 unit leg down
to create a square.
 Repeat with the 5 unit
 Find the area of each
 How do they relate to
each other?
 Thus…
a² + b² = c²
Pythagorean Triples
Consist of three positive integers a, b, and c,
such that: a 2  b2  c 2
32  42  52
Examples: 3, 4, 5
6, 8,10
5, 12, 13
Is it a right triangle?
 10, 25, 26
Does 10² + 25² = 26² ?
 6, 8, 10
Does 6² + 8² = 10² ?
Your turn…
Let’s play Pythagorean
Compared to all possible groups of
3 numbers, how many do you think
will be Pythagorean Triples?
More Pythagorean Theorem
EQ: How is a missing side of a
right triangle found?
11/13/13: Pick ONE to do. Show work!
1. If a = 7 and b = 24, what is c?
2. If a = 20 and c = 29, what is b?
This is Sheet #4!
HW check
1. How do you remember directions
like north, south, east, and west?
2. How could a map be used to
make a “right triangle”?
3. How could a ladder be used to
make a “right triangle”?
Example 1
Spanville is 40 miles north of
Mechanicsburg, and Franktown
is 120 miles east of Spanville.
How far is a direct
drive from
Franktown to
WS Problem #1
To get from point A to
point B you must avoid
walking through a
pond. To avoid the pond,
you must walk 34 meters
south and 41 meters
east. To the nearest
meter, how many meters
would be saved if it were
possible to walk through
the pond?
WS Problem #2
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 feet
90 feet
Example 3
 Mr. Yohn wants to put
an underground
sprinkler system at
MMS. 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.mathplay.com/Pythagorean-TheoremJeopardy/Pythagorean-Theorem-Jeopardy.html
 Rap: http://www.youtube.com/watch?v=DRRVuRHQWE&feature=related
 Football: http://nbclearn.com/nfl/cuecard/51220
 Cowboy’s coach: