Download 3 - dinardo

P.O.D.
Use your knowledge of
proportions to solve for x.
3 = x
8
24
3  24 = 8  x
72 = 8x
÷8 ÷8
9=x
Use your knowledge of
proportions to solve for t.
8.5
3
12.75
=
t
8.5  t = 3  12.75
8.5t = 38.25
÷8.5 ÷8.5
t = 4.5
basic
Find the values of x.
P.O.D. #
advanced
Find the values of x and y.
5 = 3
8
x
38=5x
24 = 5x
÷5 ÷5
4.8 = x
3
=
8
x
4
8x=34
8x = 12
÷8 ÷8
x = 1.5
3
=
8
2
y
3y=82
3y = 16
÷3 ÷3
y = 5.3
4-5 Similar Figures
Objective: To use proportions to find
missing lengths in similar figures
A polygon is a closed plane figure formed
by three or more line segments that do not
cross
Two polygons are similar polygons if
•Corresponding angles have the same
measure, and
•The lengths of the corresponding sides
form equivalent ratios
Similar & Congruent Figures
Figures that have the same shape but not necessarily the
same size are called similar figures.
When two figures are similar, their corresponding sides
are in proportion.
4 1
=
8 2
8
4
10
5
3
3
1
=
6
2
5
1
=
10
2
6
This means the ratios of the lengths of the
corresponding sides are equal.
The corresponding angles of similar figures are congruent.
This means the corresponding angles have
the same measure.
30°
30°
90°
90°
60°
60°
Figures that have the same shape AND size are called
congruent figures.
When two figures are congruent, the corresponding
sides are congruent AND the corresponding angles are
congruent.
Example: I do
O
D
N
C
x
4
A
6
6 = 4
9
x
B
L
6x = 49
6x = 36
÷6 ÷6
x = 6
9
M
Whiteboard:
Which side on the larger triangle corresponds to the green side
of the smaller triangle?
Whiteboard Time: We do
O
D
N
C
x
4
A
6
B
L
Which angle corresponds to Angle L?
Angle A
9
M
Whiteboard:
3
2
x
9
3 = 9
2
x
3 x = 2  9
3x = 18
÷3 ÷3
x = 6
Whiteboard:
Old Faithful in Yellowstone National Park shoots water 60 feet into the
air that casts a shadow of 42 feet. What is the height of a nearby tree
that casts a shadow 63 feet long? Assume the triangles are similar.
63 = x
42 60
63  60 = 42  x
3780 = 42x
÷42 ÷42
90 = x
Now let’s try some on our own:
Pg. 153-154 #2-18 even
Whiteboard:
1
4
1
3
1
1
≠
4
3