Similar Shapes With Examples Pp t
-
Upload
kristina-roko-evcevska -
Category
Documents
-
view
223 -
download
0
Transcript of Similar Shapes With Examples Pp t
-
8/13/2019 Similar Shapes With Examples Pp t
1/52
Similar Figures
(Not exactly the same,
but pretty close!)
-
8/13/2019 Similar Shapes With Examples Pp t
2/52
Lets do a little
review work
before discussing
similar figures.
-
8/13/2019 Similar Shapes With Examples Pp t
3/52
Congruent Figures
In order to be congruent, two
figures must be the same sizeand same shape.
-
8/13/2019 Similar Shapes With Examples Pp t
4/52
Similar Figures
Similar figures must be the
same shape, but their sizes maybe different.
-
8/13/2019 Similar Shapes With Examples Pp t
5/52
Similar Figures
This is the symbol that
means similar.
These figures are the same
shape but different sizes.
-
8/13/2019 Similar Shapes With Examples Pp t
6/52
SIZES
Although the size of the twoshapes can be different, the
sizes of the two shapes mustdiffer by a factor.
3 3
2
1
6 6
2
4
-
8/13/2019 Similar Shapes With Examples Pp t
7/52
SIZES
In this case, the factor is x 2.
3 3
2
1
6 6
2
4
-
8/13/2019 Similar Shapes With Examples Pp t
8/52
SIZES
Or you can think of the factoras 2.
3 3
2
1
6 6
2
4
-
8/13/2019 Similar Shapes With Examples Pp t
9/52
Enlargements
When you have a photographenlarged, you make a similar
photograph.
X 3
-
8/13/2019 Similar Shapes With Examples Pp t
10/52
Reductions A photograph can also be
shrunk to produce a slide.
4
-
8/13/2019 Similar Shapes With Examples Pp t
11/52
Determine the length of the
unknown side.
12
9
15
4
3
?
-
8/13/2019 Similar Shapes With Examples Pp t
12/52
These triangles differ by a factor
of 3.
12
9
15
4
3
?
15 3= 5
-
8/13/2019 Similar Shapes With Examples Pp t
13/52
Determine the length of the
unknown side.
4
2
24
?
-
8/13/2019 Similar Shapes With Examples Pp t
14/52
These dodecagons differ by a
factor of 6.
4
2
24
?
-
8/13/2019 Similar Shapes With Examples Pp t
15/52
Sometimes the factor between 2
figures is not obvious and some
calculations are necessary.
18
12 15
12
108
? =
-
8/13/2019 Similar Shapes With Examples Pp t
16/52
To find this missing factor,
divide 18 by 12.
18
12 15
12
108
? =
-
8/13/2019 Similar Shapes With Examples Pp t
17/52
18 divided by 12
= 1.5
-
8/13/2019 Similar Shapes With Examples Pp t
18/52
The value of the missing
factor is 1.5.
18
12 15
12
108
1.5 =
-
8/13/2019 Similar Shapes With Examples Pp t
19/52
When changing the size of a
figure, will the angles of the
figure also change?
? ?
?
7070
40
-
8/13/2019 Similar Shapes With Examples Pp t
20/52
Nope! Remember, the sum of all 3
angles in a triangle MUST add to 180
degrees.If the size of the
angles were
increased,the sum
would exceed
180
degrees.
70 70
40
7070
40
-
8/13/2019 Similar Shapes With Examples Pp t
21/52
70 70
40
We can verify this fact by placing
the smaller triangle inside the
larger triangle.
7070
40
-
8/13/2019 Similar Shapes With Examples Pp t
22/52
70 70
70 70
40
The 40 degree angles
are congruent.
-
8/13/2019 Similar Shapes With Examples Pp t
23/52
70 707070
70
40
40
The 70 degree angles
are congruent.
-
8/13/2019 Similar Shapes With Examples Pp t
24/52
70 707070
70
40
4
The other 70 degree
angles are congruent.
-
8/13/2019 Similar Shapes With Examples Pp t
25/52
Find the length of the missing
side.
30
40
50
6
8
?
-
8/13/2019 Similar Shapes With Examples Pp t
26/52
This looks messy. Lets
translate the two triangles.
30
40
50
6
8
?
-
8/13/2019 Similar Shapes With Examples Pp t
27/52
Now things are easier to see.
30
40
50
8
?
6
Th f t b t
-
8/13/2019 Similar Shapes With Examples Pp t
28/52
The common factor between
these triangles
is 5.
30
40
50
8
?
6
-
8/13/2019 Similar Shapes With Examples Pp t
29/52
So the length of
the missing side
is?
-
8/13/2019 Similar Shapes With Examples Pp t
30/52
Thats right! Its ten!
30
40
50
8
10
6
-
8/13/2019 Similar Shapes With Examples Pp t
31/52
Similarity is used to answer real
life questions. Suppose that you
wanted to find theheight of this tree.
-
8/13/2019 Similar Shapes With Examples Pp t
32/52
Unfortunately all that
you have is a tapemeasure, and you are
too short to reach the
top of the tree.
-
8/13/2019 Similar Shapes With Examples Pp t
33/52
You can measure the length of
the trees shadow.
10 feet
-
8/13/2019 Similar Shapes With Examples Pp t
34/52
Then, measure the length of your
shadow.
10 feet 2 feet
-
8/13/2019 Similar Shapes With Examples Pp t
35/52
-
8/13/2019 Similar Shapes With Examples Pp t
36/52
The tree must be 30 ft tall. Boy,
thats a tall tree!
10 feet 2 feet6 ft
-
8/13/2019 Similar Shapes With Examples Pp t
37/52
Similar figures work just like
equivalent fractions.
530
66 11
-
8/13/2019 Similar Shapes With Examples Pp t
38/52
These numerators and
denominators differ by a factor of
6.
530
66 11
6
6
-
8/13/2019 Similar Shapes With Examples Pp t
39/52
Two equivalent fractions are
called a proportion.
530
66 11
-
8/13/2019 Similar Shapes With Examples Pp t
40/52
Similar Figures
So, similar figures are
two figures that are thesame shape and whose
sides are proportional.
-
8/13/2019 Similar Shapes With Examples Pp t
41/52
Practice Time!
-
8/13/2019 Similar Shapes With Examples Pp t
42/52
1) Determine the missing side of
the triangle.
3
4
5
12
9
?
-
8/13/2019 Similar Shapes With Examples Pp t
43/52
1) Determine the missing side of
the triangle.
3
4
5
12
9
15
-
8/13/2019 Similar Shapes With Examples Pp t
44/52
2) Determine the missing side of
the triangle.
6
4
6 36 36
?
-
8/13/2019 Similar Shapes With Examples Pp t
45/52
2) Determine the missing side of
the triangle.
6
4
6 36 36
24
-
8/13/2019 Similar Shapes With Examples Pp t
46/52
3) Determine the missing sides of
the triangle.
39
24
33?
8
?
-
8/13/2019 Similar Shapes With Examples Pp t
47/52
3) Determine the missing sides of
the triangle.
39
24
3313
8
11
-
8/13/2019 Similar Shapes With Examples Pp t
48/52
4) Determine the height of the
lighthouse.
2.5
8
10
?
-
8/13/2019 Similar Shapes With Examples Pp t
49/52
4) Determine the height of the
lighthouse.
2.5
8
10
32
-
8/13/2019 Similar Shapes With Examples Pp t
50/52
5) Determine the height of the
car.
5
3
12
?
-
8/13/2019 Similar Shapes With Examples Pp t
51/52
5) Determine the height of the
car.
5
3
12
7.2
-
8/13/2019 Similar Shapes With Examples Pp t
52/52
THE END!