Transcript Similar Figures

Similar Figures
Let’s do a little
review work
before discussing
similar figures.
Congruent Figures
• In order to be congruent, two figures
must be the same size and same shape.

Similar Figures
• Similar figures must be the
same shape, but their sizes may
be different.

Similar Figures

This is the symbol that means
“similar.”
These figures are the same shape
but different sizes.

SIZES
• Although the size of the two shapes
can be different, the sizes of the two
shapes must differ by a factor.
4
2
3
1
3

6
6
2
SIZES
• In this case, the factor is x 2.
4
2
3
3
1

6
6
2
SIZES
• Or you can think of the factor as
2.
4
2
3
3
1

6
6
2
Enlargements
• When you have a photograph enlarged,
you make a similar photograph.

X3
Reductions
• A photograph can also be shrunk to
produce a slide.
4

The Scale factor
• A similar figure is either an enlargement or
a reduction of another figure.
• Scale factor = image length / original length
• A scale factor greater than 1 means that the
figure has been enlarged
• A scale factor between 0 and 1 means that
the figure has been reduced
Determine the length of the
unknown side.
15
12

?
4
3
9
These triangles differ by a factor of 3.
15
15
12

3= 5
?
4
3
9
Determine the length of the
unknown side.
?
2
4

24
These dodecagons differ by a
factor of 6.
?
2
4

24
Sometimes the factor between 2
figures is not obvious and some
calculations are necessary.
15
12
18

?=
8
10
12
To find this missing factor,
divide 18 by 12.
15
12
18

?=
8
10
12
18 divided by 12
= 1.5
The value of the missing
factor is 1.5.
15
12
18

1.5 =
8
10
12
When changing the size of a figure, will the
angles of the figure also change?
?
40
70
70
?
?
Nope! Remember, the sum of all 3
angles in a triangle MUST add to 180
degrees.
If the size of the
angles were
40
increased,
the sum
40
would exceed
180
degrees.
70
70
70
70
We can verify this fact by placing
the smaller triangle inside the
larger triangle.
40
40
70
70
70
70
The 40 degree angles
are congruent.
40
70
70
70
70
The 70 degree angles
are congruent.
40
40
70
70
70 70
The other 70 degree
angles are congruent.
4
40
70
7070
70
70
Find the length of the missing
side.
50
30
?
6
40
8
This looks messy. Let’s
translate the two triangles.
50
30
?
6
40
8
Now “things” are easier to see.
50
30
?
6
40
8
The common factor between
these triangles
is 5.
50
30
?
6
40
8
So the length of
the missing side
is…?
That’s right! It’s ten!
50
30
10
6
40
8
Similarity is used to answer real
life questions.
• Suppose that you wanted
to find the height of this
tree.
Unfortunately all that
you have is a tape
measure, and you are
too short to reach the
top of the tree.
You can measure the length of
the tree’s shadow.
10 feet
Then, measure the length of your
shadow.
10 feet
2 feet
If you know how tall you are,
then you can determine how tall
the tree is.
10 feet
6 ft
2 feet
The tree must be 30 ft tall. Boy,
that’s a tall tree!
10 feet
6 ft
2 feet
Similar figures “work” just like
equivalent fractions.
30
66
5
11
These numerators and
denominators differ by a factor of
6.
30
6
66
6
5
11
Two equivalent fractions are
called a proportion.
30
66
5
11
Similar Figures
• So, similar figures are
two figures that are the
same shape and whose
sides are proportional.
Practice Time!
1) Determine the missing side of
the triangle.
?
3
5
4
9
12
1) Determine the missing side of
the triangle.
15
3
5
4
9
12
2) Determine the missing side of
the triangle.
6
6
36
36
4
?
2) Determine the missing side of
the triangle.
6
6
36
36
4
24
3) Determine the missing sides of
the triangle.
39
33
?
?
8
24
3) Determine the missing sides of
the triangle.
39
33
13
11
8
24
4) Determine the height of the
lighthouse.
?
8
2.5
10
4) Determine the height of the
lighthouse.
32
8
2.5
10
5) Determine the height of the
car.
?
3
5
12
5) Determine the height of the
car.
7.2
3
5
12
THE END!