Chapter 6, Section 3: Similar Figures and Scale Drawings

Report
Similar Figures and Indirect Measurement
Review: Solve each Proportion, Round to the Nearest Tenth
Where Necessary. You may use your calculators.
2
3
f
=
21
f = 14
3
8
50
=
p
p = 133.3
z = 6.7
9
4
15
=
z
g = 3.6
16
3
19
=
g
Similar Figures
Figures that are SIMILAR have the SAME
SHAPE, but NOT necessarily the same
SIZE.
Similar Figures have the Same Angles and
Sides they are called Corresponding
Angles and Corresponding Sides.
Corresponding = The Same
These Figures Are Similar
The symbol ~ means
“is similar to”.
X
To the right,
53°
A
9
53°
ΔABC ~ ΔXYZ.
15
90°
Y
10
90°
37°
37°
12
C
Z
6
8
B
Properties of Similar Figures
The Corresponding angles have equal
measures.
 The lengths of the corresponding sides are
in proportion.

Example Problems
Parallelogram ABCD ~ parallelogram EFGH. Find the value
of X.
 Hint: Write a proportion for corresponding sides.

24
E
A
16
F
B
18
X
D
C
H
Corresponding Sides go Together.
Write the CROSS PRODUCT.
G
X
18
(X)(24) = (18)(16), X = 12
16
=
24
Try This…
Parallelogram KLMN is similar to parallelogram
ABCD in the previous example. Find the value of Y.
 Remember, X = 12 on Parallelogram ABCD.

A
16
B
21
L
Y
X
D
K
C
N
M
Indirect Measurements


Similar Figures can be used to measure
things that are difficult to measure
otherwise.
use PROPORTIONS!
Indirect Measurements

A tree casts a shadow of 10 feet long. A 5 foot
woman casts a shadow of 4 feet. The triangle
shown for the woman and her shadow is similar
to the triangle shown for the tree and its shadow.
How tall is the tree?
The tree is 12.5 feet tall.
D
REMEMBER to CHECK RATIOS!!!
THIS compared to THAT.
THIS AND THAT have to be in the
same ORDER every TIME!!!
Try This One and Draw It Yourself

A building is 70 feet high and casts a 150
foot shadow. A nearby flagpole casts a 60
foot shadow. Draw a picture/diagram of
the building, the building’s shadow, the
flagpole, and it’s shadow. Use the
triangles created to find the height of the
flagpole.
Scale Drawings
Scale Drawings are enlarged or reduced
drawings that are SIMILAR to an ACTUAL
object or place.
 The RATIO of a distance in the drawing (or
representation) to the corresponding actual
distance is the SCALE of the drawing.

Guess Where This Is…
This is the ratio for this Scale Representation!
Try This One…
The scale of the map is 50 m : 200 ft. About
how far from Robinson Road is SE 6th Ave,
if the map distance is 150m?
 Write a proportion.
 Write Cross Products.
 Simplify.


similar documents