CF5i - Using the Pythagorean Theorem
a
a2 + b2 = c2
To apply the theorem, you will need to use
your knowledge of squares & square roots.
The Pythagorean Theorem is one of the
most familiar theorems in mathematics.
b
c
Click "OK"
leg
"The sum of the squares
of the legs in a right
triangle is equal to the
square of it's hypotenuse."
leg
hypotenuse
Lets test your knowledge of squares & square roots.
42=
72=
122=
152=
252=
Type in your answers
√81=
√25=
√100=
√121=
√64=
Look over the example and then try some on your own.
√a2  = √36
a2  =   36
a   =    6
Inverse operations must be used when solving
for a missing side of a right triangle.
The inverse operation for squaring a value is
square rooting.
example:
Notice how the
square & the square
root cancelled each
other out.
Type in your answers
b2 = 4
b =
try outs:
c2 = 400
c =
Now that we have reviewed the skills needed to apply
the Pythagorean Theorem, let's get down business.
Look at the given triangle below.
See if you can identify & label the triangle correctly.
"a" for the short leg.
"b" for the other leg.
"c" for the hypptenuse.
Type in your answers.
a
If you labeled your triangle like below,
then you were correct.
b
"a" for the short leg.
"b" for the other leg.
"c" for the hypptenuse.
c
Click "OK"
b
a
c
-9            -9  
32+b2 =  52
a2+b2 = c2
9 +b2 = 25
Now that you can correctly label a right triangle,
let's get started with finding a missing side.
√b2=√16
b2=  16
b=4
c=5
b=?
Set up the equation
Simplify
Solve using inverse operations
a=3
Type in your answers
a=9
     2+    2 =     2
a2+ b2  =  c2
+ b2  =
b=?
b2  =
c=15
b  =
Finding the missing side.
Solve using
inverse operations
Simplify
Set up the equation
     2+     2 =       2
a2 +        =
a2+ b2  =  c2
Type in your answers
a2  =
a   =
c=10
b=8
a=?
Finding the missing side.
Simplify
Solve using
inverse operations
Set up the equation
     2+      2 =     2
     +         =  c2
a2+  b2  =  c2
Type in your answers
c  =
=  c2
=  c
c=?
b=16
a=12
Finding the missing side.
Simplify
Solve using
inverse operations
Set up the equation
     2+      2 =     2
     +         =  c2
a2+  b2  =  c2
Type in your answers
c  =
=  c2
=  c
c=?
b=24
a=18
Cynthia drove 56 miles due south and 90 miles due
west. If she drove in a straight line back to the point
where she started, how far will she drive?
146
You are now ready for the final question!
106
Choose the best answer
? miles
90 miles
70
56 miles
11236
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