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Applications: Pythagorean Theorem Notes
Key Concept: Identifying Parts of Triangle:
• Legs: 2 sides forming right angle (a, b)
• Hypotenuse: side opposite the right angle; longest side of triangle
(c)
Leg (a) {N hypotenuse (c)
f
l
eg (b)
Example: Identifying Parts of Triangle
identify the legs and hypotenuse of the foiiowing right triangles:
17
Legs: 8, 15
(make up right L)
8
Hypotenuse: 17 (largest # & opposite right L)
Provided below are lengths of a right triangle. Identify the legs and
hypotenuse.
• 6,10, 8
Hypotenuse: 10 (largest), Legs: 6 and 8
• 9, 12, 15 Hypotenuse: 15 (largest), Legs: 9 and 12
Practice: Identifying Parts of Triangle
Identify the legs and hypotenuse of the following right triangles:
5
3
30
Provided below are lengths of a right triangle. Identify the legs and
hypotenuse.
a. 12,13, 5 Hypotenuse:____ Legs:
and
b. 9, 12, 15 Hypotenuse:____ Legs:
and
c. 25, 7, 24 Hypotenuse:___ Legs:
and
App: Pythagorean Theorem
I
Applications: Pythagorean Theorem Notes
Key Concept: Pythagorean Theorem
2 (for right angles)
2 =c
2+b
o Pythagorean theorem: a
• Pythagorean Theorem is used to find the length of a side of a right
triangle when the lengths of the other 2 sides are known.
-‘-C=3
D=41
2
2
2
e
then
2
2
iTa-s-D=c
iT3+4-= D
then
f=\/52=5
2
\/U+h_C_C
a=3
or
or
if
32 =
then 3
if a
2
5242
=
then a
=
-
=
2
a
2
b
=
Examples: Solve for Missing Side
Using the Pythagorean Theorem, solve for the missing side:
x
6
Step 1: Identify legs & hypotenuse
Hypotenuse: c = x, Legs: a=6, b=8
8
Step 2: Pluq in values
62 + 8= x
2
in a
2
+
2
b
=
2 and solve
c
64=x
2
36+
100=x
2
10 =x
Step 1: identify legs & hypotenuse
Hypotenuse: c = 17, Legs: ax, b15
x
h
15
Step 2: Plug in values
= 172 52
289 -225
=64
2
x
x=8
=
App: Pythagorean Theorem
in a
2
=
-
2 and solve
b
Applications: Pythagorean Theorem Notes
Practice: Solve for Missing Side
Using the Fythagorean Theorem, solve for the missing side:
1. Solve for a
2. Solve for c
10
3. Solve for b
24
2
C
b
4. Solve for a
10
a
5. Solve for c
5
6. Solve for b
4
b
Key Concept: Determining if lengths are sides of right triangle
. When given 3 sides, identify your hypotenuse and legs with
the
.
.
hypotenuse being the largest number,
Plug in values into the Pythagorean Theorem: a
2+b
2
If the equation is true, then you have a right triangle
=
Examples: Determining if lengths are sides of right triangle
Determine whether the given lengths are sides of a right triangle.
a.3,9,6
b.6,1O,8
h’potenuse: 9; legs: 3, 6
hypotenuse: 10; legs 6, 8
3+62=92
64÷82=102
9+36=81
45 81
No
36+64=100
100 =100
Yes
App: Pythagorean Theorem
3
Applications: Pythagorean Theorem Notes
Practice: Determining if lengths are sides of right triangle
Determine whether the given lengths are sides of a right triangle.
c.7,24,25
b16,30,34
a20,21,29
d. 24, 60, 66
e. 23,18,14
f. 9, 12, 15
Key Concept: Pythagorean Triples
There are many common sets of 3 whole numbers that satisfy the
Pythagorean Theorem. Memorize the following Pythagorean Triples. They
corn•e in handy and help save you time.
• 3,4,5
.5,12,13
• 7,24,25
• 8,15,17
NOTE: The largest number must be the hypotenuse in order for these to
work.
Key Concept: Special Right Triangles
//4\
I
App: Pythagorean Theorem
4
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