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Review on Proportions
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Review on Proportions
Two fractions that are equal a=
re
said to be
proportional <=
/span>.
Review on Proportions
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Review on Proportions
Two fractions that are equal a=
re
said to be
proportional <=
/span>. That is, if =
;
then and
are proportional.
a
b
c
d ,
=3D
a
b
c
d
Review on Proportions
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Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Given a propotion =
;
the equality still hold if
any factor is multiplied across diagonally.
Two fractions that are equal a=
re
said to be
proportional <=
/span>. That is, if =
;
then and
are proportional.
a
b
c
d ,
=3D
a
b
c
d
a
b
c
d ,
=3D
Review on Proportions
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Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Given a propotion =
;
the equality still hold if
any factor is multiplied across diagonally.
Two fractions that are equal a=
re
said to be
proportional <=
/span>. That is, if =
;
then and
are proportional.
a
b
c
d ,
=3D
a
b
c
d
a
b
c
d ,
=3D
Example A: Solve=
for
x.
x
3
4
5
=3D
Review on Proportions
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Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Given a propotion =
;
the equality still hold if
any factor is multiplied across diagonally.
Two fractions that are equal a=
re
said to be
proportional <=
/span>. That is, if =
;
then and
are proportional.
a
b
c
d ,
=3D
a
b
c
d
a
b
c
d ,
=3D
Example A: Solve=
for
x.
x
3
4
5
=3D
Review on Proportions
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0018.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Given a propotion =
;
the equality still hold if
any factor is multiplied across diagonally.
Two fractions that are equal a=
re
said to be
proportional <=
/span>. That is, if =
;
then and
are proportional.
a
b
c
d ,
=3D
a
b
c
d
a
b
c
d ,
=3D
Example A: Solve=
for
x.
x
3
4
5
=3D
Review on Proportions
x
3 * 4
5
=3D
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Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Given a propotion =
;
the equality still hold if
any factor is multiplied across diagonally.
Two fractions that are equal a=
re
said to be
proportional <=
/span>. That is, if =
;
then and
are proportional.
a
b
c
d ,
=3D
a
b
c
d
a
b
c
d ,
=3D
Example A: Solve=
for
x.
x
3
4
5
=3D
Review on Proportions
x
3 * 4
5
=3D
12
5
=3D
=3D
2
2
5
Example B: Solve=
for
x.
3
x
4
=3D
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Review on Proportions
Given a propotion =
;
the equality still hold if
any factor is multiplied across diagonally.
Two fractions that are equal a=
re
said to be
proportional <=
/span>. That is, if =
;
then and
are proportional.
a
b
c
d ,
=3D
a
b
c
d
a
b
c
d ,
=3D
Example A: Solve=
for
x.
x
3
4
5
=3D
Review on Proportions
x
3 * 4
5
=3D
12
5
=3D
=3D
2
2
5
Example B: Solve=
for
x.
3
x
4
=3D
3
x
4
=3D
1
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Review on Proportions
Given a propotion =
;
the equality still hold if
any factor is multiplied across diagonally.
Two fractions that are equal a=
re
said to be
proportional <=
/span>. That is, if =
;
then and
are proportional.
a
b
c
d ,
=3D
a
b
c
d
a
b
c
d ,
=3D
Example A: Solve=
for
x.
x
3
4
5
=3D
Review on Proportions
x
3 * 4
5
=3D
12
5
=3D
=3D
2
2
5
Example B: Solve=
for
x.
3
x
4
=3D
3
x
4
=3D
1
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Review on Proportions
Given a propotion =
;
the equality still hold if
any factor is multiplied across diagonally.
Two fractions that are equal a=
re
said to be
proportional <=
/span>. That is, if =
;
then and
are proportional.
a
b
c
d ,
=3D
a
b
c
d
a
b
c
d ,
=3D
Example A: Solve=
for
x.
x
3
4
5
=3D
Review on Proportions
x
3 * 4
5
=3D
12
5
=3D
=3D
2
2
5
Example B: Solve=
for
x.
3
x
4
=3D
3
x
4
=3D
1
x
=3D
3
4
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Review on Proportions
Fact About Simil=
ar
Triangles
The corresponding sides of two similar (same shape)
triangles=
are
proportional.
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Review on Proportions
Fact About Simil=
ar
Triangles
The corresponding sides of two similar (same shape)
triangles=
are
proportional.
There're many ways to set up the proportions in
the
figure shown below:
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0024.htm
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Review on Proportions
Fact About Simil=
ar
Triangles
The corresponding sides of two similar (same shape)
triangles=
are
proportional.
There're many ways to set up the proportions in
the
figure shown below:
x
X
y
Y
=3D
z
Z ,
=3D
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0025.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Fact About Simil=
ar
Triangles
The corresponding sides of two similar (same shape)
triangles=
are
proportional.
There're many ways to set up the proportions in
the
figure shown below:
x
X
y
Y
=3D
z
Z ,
=3D
x
y
X
Y,
=3D
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0026.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Fact About Simil=
ar
Triangles
The corresponding sides of two similar (same shape)
triangles=
are
proportional.
There're many ways to set up the proportions in
the
figure shown below:
x
X
y
Y
=3D
z
Z ,
=3D
x
y
X
Y,
=3D
z
x
Z
X ,
=3D
̷=
0;
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Review on Proportions
Examples of Simi=
lar
Triangles
The following two case=
s of
similar triangles show up often:
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Review on Proportions
Examples of Simi=
lar
Triangles
I. Given =
that DE
is parallel to
AB, then =
ΔABC is si=
milar to
Δ DEC.
The following two case=
s of
similar triangles show up often:
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Review on Proportions
Ó F r a n k M a
2 0 0 6
Examples of Simi=
lar
Triangles
I. Given =
that DE
is parallel to
AB, then =
ΔABC is si=
milar to
Δ DEC.
II. Given=
that DE
is parallel
to
AB, then Δ ABC is si=
milar to ΔDEC.
The following two case=
s of
similar triangles show up often:
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0010.htm
Content-Transfer-Encoding: quoted-printable
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Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0029.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
6
x
+ 6
5
3
=3D
By
similar triangles,
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0030.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
6
x
+ 6
5
3
=3D
By
similar triangles,
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0032.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
6
x
+ 6
5
3
=3D
By
similar triangles,
x
+ 6
6 * 5
3
=3D
=3D
10
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0033.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
6
x
+ 6
5
3
=3D
By
similar triangles,
x
+ 6
6 * 5
3
=3D
=3D
10
So
x =3D 4
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0034.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
6
x
+ 6
5
3
=3D
By
similar triangles,
x
+ 6
6 * 5
3
=3D
=3D
10
So
x =3D 4
Example D: Find x, assuming
the sides are parallel.
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0040.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
6
x
+ 6
5
3
=3D
By
similar triangles,
x
+ 6
6 * 5
3
=3D
=3D
10
So
x =3D 4
Example D: Find x, assuming
the sides are parallel.
By
similar triangles,
x
x
+ 5
10
4
=3D
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0042.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
6
x
+ 6
5
3
=3D
By
similar triangles,
x
+ 6
6 * 5
3
=3D
=3D
10
So
x =3D 4
Example D: Find x, assuming
the sides are parallel.
By
similar triangles,
x
x
+ 5
10
4
=3D
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0043.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
6
x
+ 6
5
3
=3D
By
similar triangles,
x
+ 6
6 * 5
3
=3D
=3D
10
So
x =3D 4
Example D: Find x, assuming
the sides are parallel.
By
similar triangles,
x
x
+ 5
10
4
=3D
4(x
+ 5) =3D 10x
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0044.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
6
x
+ 6
5
3
=3D
By
similar triangles,
x
+ 6
6 * 5
3
=3D
=3D
10
So
x =3D 4
Example D: Find x, assuming
the sides are parallel.
By
similar triangles,
x
x
+ 5
10
4
=3D
4(x
+ 5) =3D 10x
4x
+ 20 =3D 10x
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Content-Location: file:///C:/AA8CB117/0Review_files/slide0045.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Review on Proportions
Examples of Simi=
lar
Triangles
Example C: Fi=
nd x,
assuming the sides
are parallel.
6
x
+ 6
5
3
=3D
By
similar triangles,
x
+ 6
6 * 5
3
=3D
=3D
10
So
x =3D 4
Example D: Find x, assuming
the sides are parallel.
By
similar triangles,
x
x
+ 5
10
4
=3D
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