Transcript Are the polygons similar?

Lesson 6.1
Use Similar Polygons
• Two figures that have the same
shape but not necessarily the same
size are similar (~).Two polygons are
similar if (1) corresponding angles are
congruent and (2) corresponding
sides are proportional. The ratio of
the lengths of corresponding sides is
the similarity ratio.
What is a similarity
statement?
• A statement that two polygons are
similar. (It is similar (tee hee) to a
congruency statement)
• Example:
Scale Factor
• You might hear this referred to as
the similarity ratio.
• This is the ratio of the lengths of
the corresponding sides of two
similar polygons.
• The scale factor depends on the
order of comparison.
Are the polygons similar? If they are, write
a similarity statement, and give the
similarity ratio. If they are not, explain.
Triangle ABC is similar to triangle XYZ and the similarity ratio
Is 2/1 or Triangle xyz is similar to abc and the similarity ratio
1/2
Are the polygons similar? If they are, write
a similarity statement, and give the
similarity ratio. If they are not, explain.
These are not similar because the angles are not congruent
<I
<O
<J
NO
LO
LO
Algebra The polygons are similar.
Find the value of the variable.
If you think x=3.96 feet, you are correct
Algebra You can use similarity to
find perimeter as well. These
two rectangles are similar as
they appear. Find the perimeter
of each
PQRS perimeter: 26 inches, LMNO perimeter:15.6 inches
Perimeter of Similar
Polygons
2/3
53
7.5
4.5
53
37
5
• In any golden rectangle, the length and width are
in the golden ratio which is about 1.618 : 1
• The golden rectangle is considered pleasing to the
human eye. It has appeared in architecture and
art since ancient times. It has intrigued artists
including Leonardo da Vinci (1452–1519). Da Vinci
illustrated The Divine Proportion, a book about
the golden rectangle.
• A golden rectangle is a rectangle
that can be divided into a square and
a rectangle that is similar to the
original rectangle. A pattern of
repeated golden rectangles is shown
to the right. Each golden rectangle
that is formed is copied and divided
again. Each golden rectangle is
similar to the original rectangle.
This Gold rectangle is not a golden rectangle
Application of GR
• The length and width of a rectangular
tabletop are in the golden ratio. The
shorter side is 40 in. Find the length of
the longer side.
64.72 inches