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The Pythagorean Theorem
Mathematics, Grade 7
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Study Guide The Pythagorean Theorem Mathematics, Grade 7
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THE
PYTHAGOREAN
THEOREM
What
Is
the
Pythagorean
Theorem?
The
Pythagorean
Theorem
is
a
theorem
that
states
the
sum
of
the
squares
of
the
legs
of
a
right
triangle
equals
the
square
of
the
length
of
the
hypotenuse.
•
In
mathematical
terms,
this
is
represented
by
a² +
b² =
c²,
where
a
and
b
are
the
length
of
the
legs
and
c
is
the
length
of
the
hypotenuse
of
a
right
triangle.
•
A
Pythagorean
triple
is
a
set
of
numbers
that
always
satisfy
the
equation,
a² +
b² =
c².
•
By
using
the
Pythagorean
Theorem,
a
triangle
can
be
determined
to
be
a
right
triangle.
Also
if
either
the
legs
or
a
leg
and
hypotenuse
of
a
right
triangle
are
given,
the
Pythagorean
theorem
can
be
used
to
find
the
missing
leg
or
hypotenuse.
In
order
to
use
the
Pythagorean
Theorem,
it
is
important
to
know
how
to
evaluate
a
power.
A
power
is
a
number
in
the
form
of
x²,
which
means
x
squared
or
x
·
x.
With
the
Pythagorean
Theorem,
a
number
will
be
equal
to
c²,
for
example,
and
need
to
be
solved
for
c.
In
order
to
solve
for
c,
the
square
root
must
be
taken.
The
square
root
of
a
number
is
equal
to
a
number
that,
when
multiplied
by
itself,
will
produce
the
given
number.
The
Pythagorean
Theorem
can
be
applied
to
any
right
triangle.
Many
everyday
items
can
be
evaluated
using
the
Pythagorean
Theorem.
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
How
to
use
the
Pythagorean
Theorem
In
order
to
use
the
Pythagorean
Theorem,
powers
and
roots
should
be
looked
at
first.
For
example,
what
is
7²
and
the
square
root
of
225?
Ex.
7²
=
7
· 7
=
49
The
square
root
of
225
=
√225
=
15
because
15
·
15
=
225.
The
Pythagorean
Theorem
can
only
be
used
if
a
triangle
is
a
right
triangle.
This
would
have
to
be
stated
in
order
to
use
the
Pythagorean
Theorem.
If
a
triangle
is
a
right
triangle
and
the
sides
are
given,
the
hypotenuse
can
be
found
as
follows:
Ex.
A
right
triangle
has
sides
of
6
cm
and
8
cm.
a² +
b² =
c²
6² +
8² =
c²
36
+
64
=
c²
100
=
c²
√100
=
c²
;
c
=10
The
hypotenuse
of
the
triangle
is
10
cm.
The
Pythagorean
Theorem
can
also
be
used
if
one
leg
and
the
hypotenuse
are
given
to
get
the
missing
leg.
The
Pythagorean
Theorem
is
also
used
to
prove
that
triangles
are
right
triangles.
•
For
example
if
a
triangle
has
legs
that
are
5
cm
and
10
cm
and
a
hypotenuse
of
15,
is
the
triangle
a
right
triangle?
Ex.
a² +
b² =
c²
5²
+
10²
=
15²
25
+
100
=
225
125
≠
225
so
the
triangle
is
not
a
right
triangle.
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
Objects
in
every
day
life
can
be
used
with
the
Pythagorean
Theorem
also.
•
For
example,
if
an
18
ft
ladder
leans
against
a
house
and
rests
on
the
house16
ft
above
the
ground,
how
far
away
is
the
ladder
from
the
house
given
that
the
house
and
the
ground
make
a
right
angle?
Ex.
a² +
b² =
c²
a²
+
16²
=
18²
a²
+
256
=
324
a²
=
68
a
=
√68
≈
8.25
≈
8.3
ft.
The
ladder
is
approximately
8.3
ft
away
from
the
house.
Try
This!
1.
What
is
8³?
2.
What
is
the
square
root
of
3600?
3.
A
triangle
is
a
right
triangle.
The
legs
are
8
cm
and
14
cm.
What
is
the
length
of
the
hypotenuse?
4.
A
right
triangle
has
a
hypotenuse
of
26
ft
and
a
leg
that
is
24
ft.
What
is
the
length
of
the
missing
leg?
5.
A
triangle
has
sides
of
5
cm
and
8
cm.
The
hypotenuse
is
13.
Is
the
triangle
a
right
triangle?
6.
A
square
is
cut
into
two
triangles
by
a
diagonal.
If
a
side
of
the
square
measures
10
m,
what
is
the
length
of
the
diagonal?
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
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