Transcript Similar Figures

Similar Figures
(Not exactly the same,
but pretty close!)
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 shapes4must
differ by a factor.
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

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
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
Solving for the Missing Side
Using Proportions
• One more way to solve proportions:
• 2=6
8 n
2xn=6x8
2n = 48
2
2
n = 24
n
8
6
2
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
Step 1
B
• Draw a right triangle.
Label each angle.
Cut out the triangle.
A
C
Step 2
• Cut off the angles as shown. B
A
C
Step 3
• Place the angles together at a point to form
a straight line.
A
B
C
B
A
C
The angles placed together form a
straight line.
A straight line or straight angle is
equal to 180º.
Therefore, the sum of all the angles in
a triangle is equal to 180!º
You can use this fact to find the missing
angle in a triangle.
For example, lets say I have the
following triangle:
?
80º 45º
I know the measurements of two of the
angles, but the third one is a mystery. How
do I find the measurement of that third
angle?
Remember that all the angles in a
triangle added together equal 180.º
?
So: 80º + 45º + ? º = 180º
It’s an equation!
Step
1:
Add
80º
+
45º
80º 45º
125º + ?º = 180º
Step 2: Subtract 125º from both sides
?º = 55º
Answer!
√ Check: 80º + 45º + 55º = 180º
Lets try another:
24º
?º
32º
32º + 24º + ?º = 180º
Step 1: Add 32º + 24º
56º + ?º = 180º
Step 2: Subtract 56º from both sides
?º = 124º Answer!
√ Check: 32º + 24º + 124º = 180º
This one is a bit tricky...but I think you ca
Hmmm....this one has a 45º
45º angle, a mystery
angle, and an angle with a
square corner.
?º
When you remember what
that square corner means, put
your finger by your nose.
(Remember: no nose picking
allowed!)
Yes! The square corner means that it is a right angle.
I know that a right angle is
equal to 90.º
45º
?º
So... 45º + 90º + ?º = 180º
Step 1: Add 45º + 90º
135º + ?º = 180º
Step 2: Subtract 135º from both sides
?º = 45º
Answer!
√ Check: 45 + 90º + 45º = 180º
THE END!