Transcript Right Triangles - Floyd County Public Schools

Right Triangles
Prepared by Title V Staff:
Daniel Judge, Instructor
Ken Saita, Program Specialist
East Los Angeles College
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© 2002 East Los Angeles College. All rights reserved.
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Consider the Right Triangle.
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If we draw a vertical line from vertex C
to a point D on our base AB , we form
other right triangles.
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We have now created three right
triangles ABC, ACD, and CBD.
These triangles are all similar!
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Recall that similar triangles have
congruent (equal measure)
corresponding angles.
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Claim:    ,   




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We know the following
    90
but,     90 as well
so,       
   
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Similarly,
    90
but,     90
      
  
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Our picture becomes. . .
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Notice we can dissect this right triangle.
We must rotate the first right triangle ¼
turn clockwise so the two triangles
have the same alignment.
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Since these triangles are similar, the
following properties can be used.
AD CD AD CD DC DB

;

;

AC CB DC DB AC CB
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It can be shown that the original right
triangle ABC is similar to the smaller
two right triangles.
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If we separate the figure into three
triangles and use the same alignment
for all three we get . . .
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B
B
C
C
A
D
A
D
C
Similar proportions can be created.
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Example 1) Determine the value for X
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AD AC  short leg
Since

AC AB  hypotenuse
X 10
we have

solving for X,
10 25
10
X  10 
25
100
X
25
X4
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We really have
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Example 2)
AC CD  short leg

CB CA  hypotenuse
X 4
becomes
 ; X2  16(4); X2  64
16 X
X   64; X  8
X8
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Example 3)
8  short leg


long
leg
18 X
2
2
X  8(18); X  144; X   144
X
X  12; X  12
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Example 4)
X  short leg


long
leg
X5 6
2
2
36  X(X  5); 36  X  5X; X  5X  36  0
6
(X  9)(X  4)  0
X9 0
X4 0
X  9
X4
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Summary
AD AC

AC CB
Short Leg
Hypotenuse
DB CB

CB AB
Long Leg
Hypotenuse
AD CD

CD DB
Short Leg
Long leg
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End of Right Triangles
Title V
East Los Angeles College
1301 Avenida Cesar Chavez
Monterey Park, CA 91754
Phone: (323) 265-8784
Email Us At:
[email protected]
Our Website:
http://www.matematicamente.org
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