Transcript Proportions and Similarity

Advanced Geometry
Similarity
Lesson 2
Proportions & Similarity
Ratio
a
b
The ratio of a to b can be expressed as ,
where b is not zero.
FORMS:
1 to 2
1: 2
1
2
All ratios must be in simplest form.
24
3

8
1
32 : 6
16 : 3
A ratio in which the denominator is 1 is
called a unit ratio.
EXAMPLE:
The number of students that participate in sports
programs at Central High School is 550. The total
number of students in the school is 1850. Find the
athlete to non-athlete ratio.
4 x  5 26

3
6
x  2
3x  5
1

5
x 3
An extended ratio is a ratio used to compare three
or more numbers.
Extended ratios are written using colons.
EXAMPLE:
In a triangle, the ratio of the measures of three angles is
1 1 1
: : . Find the measures of the angles of the triangle.
3 4 6
Example:
The ratios of the sides of three polygons are given. Make
a conjecture about the type of each polygon described.
2:2:3
3: 3: 3: 3
Isosceles
triangle
Rhombus
4:5:4:5
Similar Polygons
In order for two polygons to be similar,
all of their corresponding angles must be congruent and
all of the corresponding sides must form a proportion.
A
B
D
F
C
E
Similarity Statement:
A  E
B  F
C  D
AB BC AC


EF FD ED
EXAMPLES:
Determine whether each pair of figures is similar. Justify
your answer.
No; the
corresponding angles
are not congruent.
EXAMPLE:
An architect prepared a 12-inch model of a skyscraper to
look like an actual 1100-foot building. What is the scale
factor of the model compared to the actual building?
EXAMPLE:
Each pair of polygons is similar. Write a similarity
statement, find x, y, ED, and the scale factor.