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GeoA -Lesson- Pythagorean Theorem
供稿人: Hampton
(原作者: Warren)
Right Triangle Fun!
1. Get out a piece of paper.
2. Get out a pencil or pen.
3. Get out a calculator.
Read each slide.
Answer the questions
The Pythagorean Theorem can be used
to find the length of the missing side of
a right triangle if you know the length
of the other two sides.
5
12
X
What kind of triangles does the Pythagorean
Theorem work on?
***  You can click the back button << to see
the previous slide if you want to!
Acute Triangles
Right Triangles
Obtuse Triangles
Any kind of triangle
The formula for the Pythagorean Theorem is:
           leg2 + leg2 = hypotenuse2
5
12
X
What in the world are
Legs or Hypotenuse?
Legs always make a right angle!
They Hypotenuse must be the longest!
L
E
G
H
Y
P
LEG
O
T
E
N
U
S
E
L
E
G
H
Y
P
LEG
O
T
E
N
Which side must be
the longest?
U
S
E
leg
hypotenuse
It doesn't matter which way the triangle is facing.
The legs always make the right angle
and the side opposite the right angle
is always the hypotenuse.
hypotenuse
leg
leg
z
Which side is the hypotenuse?
(click on the correct answer)
x
x
y
y
z
z
If you picked y, you were correct!!!
x
x
y
y
z
Which side is the hypotenuse?
(click on the correct answer)
x
z
y
x
z
y
Did you pick the right answer?
x
z
x
y
None of these, it's not a right triangle!
Which side is the hypotenuse?
(click on the correct answer)
x
z
y
x
z
y
Just because it looks like a right triangle, doesn't
mean it is. It has to be marked or labeled or some
way let you know there is a right angle!
Did you catch my trickery?
z
x
y
So how do we use this
Pythagorean Theorem to find
the missing side of a right triangle?

Well, we've covered the first step already.
First we have to identify the legs and the
hypotenuse.


The legs have lengths 3 and 4 and we don't
know how long the hypotenuse is.
x
4
3
Once we've identified the legs and hypotenuse,
we substitute these for the letters in the formula.
leg2 + leg2 = hyp2

(3)2 + (4)2 = (x)2 

x
4
3
So the hypotenuse is 5!
Simplify and Solve

First the exponents
(3)2 + (4)2 = (x)2

 9    + 16  = x2
            25 = x2   
         √25 =√x2
            5   =  x
Write this equation on your paper and solve.

Make sure you show all your work!
52 + x2 = 132
Type your answer below!
x =
Did you get the right answer? Here's my work:


52 + x2 = 132
25 + x2 = 169
-25            -25
        x2  = 144
        x    =√144
        x    = 12
Which side is the hypotenuse?
x
40
41
They're all hypotenuses!
There isn't a hypotenuse!
x
40
41
Formula: leg2 + leg2 = hyp2
So the missing leg has a length of 9!
41 was the correct answer!
x
x2   +   402  =   412
x2   +  1600 =  1681
       - 1600       -1600
x2                 =  81
x                   = 9
40
41
Now you try one:







Which way should you set up the equation?  
                 (Pick one)


(8)2 + (6)2 = (n)2
6
8
n
(6)2 + (n)2 = (8)2
If you picked: (8)2 + (6)2 = (n)2
               YOU'RE CORRECT!!!
You could also write: (6)2 + (8)2 = (n)2
Write down the equation
          on your paper.

      (6)2 + (8)2 = (n)2

Which  one of these show up in your work?
Now solve your equation.
  28 = n2
  100 = n2
  196 = n2
How long is the hypotenuse (c)?
               PICK ONE
100
50
10
100 = n2
is CORRECT!!!
√10 = √n2
10 = n
The hypontenuse is 10 units long.

(15)2 + (17)2 = (x)2
Now you try one:
Which equation is correct?    (Pick one)
15
17
(15)2 + (x)2 = (17)2
x
Which equation shows up in your work?
If you picked: (15)2 + (x)2 = (17)2
               YOU'RE CORRECT!!!
You could also write: (x)2 + (15)2 = (17)2
  x2 = 22
 x2 = 352
x2 = 64
x = 8 which means
the leg is 8 units long!
x2 = 64 is CORRECT!
So, which answer is correct?
15
17
x = 8 which means
the hypotenuse is 8
units long!
x
x = 8 which means
the leg is 8 units long
is the correct answer!
15
17
x
Let's try one more:







Which way should you substitute the numbers?                          (Pick one)

(13)2 + (5)2 = (m)2
13
5
m
(m)2 + (5)2 = (13)2
Which is the correct simplification of the equation?                                (PICK ONE)
If you picked: (m)2 + (5)2 = (13)2
               YOU'RE CORRECT!!!
You could also write: (5)2 + (m)2 = (13)2
  m2 + 25 = 169
  m2 + 10 = 26
What is the next step and the result?                   PICK ONE
  Subtract 25.      m2 = 144
  Take the square root of both sides.     
       m + 5 = 13
m2 + 25 = 169 is CORRECT!!!
13
5
m
  You must subtract 25.      m2 = 144
  m =72 units
  m =12 units
  m =144 units
√m2 = √144
m = 12
The leg is 12 units long.

Which equation is correct?
What letter or number
is on the hypotenuse?
What's the final answer for x?
x2 + 802 = 642
x2 + 642 = 802
642 + 802 = x2
64
80
x
Which equation is correct?
What letter or number
is on the hypotenuse?
What's the final answer for x?
x2 + 642 = 802
80
64
48
80
x
Which equation is correct?
What letter or number
is on the hypotenuse?
What's the final answer for x?
x2 + 1442 = 172
x2 + 172 = 1442
172 + 1442 = x2
x
17
144
Which equation is correct?
What letter or number
is on the hypotenuse?
What's the final answer for x?
x2 + 452 = 362
x2 + 362 = 452
362 + 452 = x2
36
45
x
Which equation is correct?
What letter or number
is on the hypotenuse?
What's the final answer for x?
x2 + 602 = 112
x2 + 112 = 602
112 + 602 = x2
60
x
11
The first equation should be x2 +252 =242
It's not a right triangle, so you can't use
     the Pythagorean Theorem
The  x2 =49 is wrong.
I Have no idea
x2 +242 =252
x2 +576=625
x2          =49
x            = 7
Why is this problem WRONG?
24
25
x
Which equation is correct?
What letter or number
is on the hypotenuse?
What's the final answer for x?
x2 + 162 = 342
x2 + 342 = 162
162 + 342 = x2
x
34
16
Which equation is correct?
What letter or number
is on the hypotenuse?
What's the final answer for x?
x2 + 22.52 = 142
x2 + 142 = 22.52
142 + 22.52 = x2
22.5
x
14
The first equation should be 62 +102 =x2
It's not a right triangle, so you can't use
     the Pythagorean Theorem
The  102 - 62 isn't 42.
I Have no idea
x2 +62 =102
x2        =102 -62
x2        =42
x          = 16
Why is this problem WRONG?
x
90
10
6
The first equation should be 32 +x2 =42
It's not a right triangle, so you can't use
     the Pythagorean Theorem
The  x2 =25 is wrong.
I Have no idea
32 +42 =x2
25        =x2
5          =x

Why is this problem WRONG?
4
25
x
3
70
Which equation is correct?
What letter or number
is on the hypotenuse?
What's the final answer for x?
x2 + 20.82 = 56.082
x2 + 56.082 = 20.82
20.82 + 56.082 = x2
20.8
56.08
x
35
The next set of problems have a Right
Triangle in them somewhere, so you'll
have to find the triangle to solve it!
45
What Kind of Triangle is this?
Acute Triangle
Right Triangle
Obtuse Triangle
Not enough info
How big is y
?
20∘
How big is x?
x
y
9
How big is ∡a?
15
a
Find x first!
What kind of
triangle is ∆ABC?
What is the value of y?
x =
A
x
B
8
17
31.76
30.76
28
None of these
D
y
20
C
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