Transcript Unit 4: Similarity

Warm Up
1. Write your own definition for similar objects.
2. What was the most difficult problem from yesterday’s test?
3. Many of you have come up with plans to do better on
upcoming units. Are you doing these things? What can you
do to continue to better prepare yourself during this new
unit?
Unit 4 – Essential Questions
 How can we use proportions and their relationships
to describe similar figures?
 What theorems can we use to prove triangles similar?
Bonus Question
 Hannelmore Kraus of Frankfurt, Germany, stopped the development
of a skyscaper because she wanted her apartment to get its fair
amount of sunlight. To halt the construction she used a German law
that specifies that every homeowner is entilted to sunlight.
 Kraus was offered 1.6 million dollars to drop her lawsuit, but she
refused. The skyscraper was scheduled to be 265 m tall and was to
be built 60 m from Kraus’s apartment.
 Explain how Hannelore Kraus could use indirect measurement to
estimate the length of the shadow of the building at a particular
time of day.
Unit 4 – Day 1
 Objectives
 To write ratios and solve proportions
 To identify similar polygons
 To apply similar polygons
8.1 Ratios and Proportions
 A ratio is a comparison of two quantities.
 a to b
 a:b

a
, b ≠ 0.
b
 A proportion is a statement that two ratios are equal.

a c
=
b d
or
Properties of Proportions
If
then ad=bc (Cross Product Property)
**Used when solving for a variable!
Other Properties:
If
, then…
Example – Solve
1.
Example – Solve
2.
Example – Solve
3.
Which is equivalent?
h k
Which of the following proportions is equivalent to: =
j m
1.
2.
j k
=
h m
m k
=
j h
3.
4.
k m
=
j h
j+k m+ j
=
j
h
8.2 Similar Polygons
 Similar Polygons - Two figures that
have the same shape but not
necessarily the same size
 Symbol: ~
Similar Polygons
 Two polygons are similar if and only if:
Corresponding angles are congruent
AND
2. Corresponding sides are proportional
Example:
1.
Similarity Ratio
 The ratio of the lengths of corresponding sides is the
Similarity Ratio
 The Similarity Ratio compares one object to another
Similarity Ratio = 5:15 = 1:3
5
15
Scale Factor
 A Scale Factor is the number that you multiply by to resize a
figure (make bigger or smaller)
 Review from Unit 1:
(x, y) ® (cx, cy)
In this algebraic rule for dilation, c is the scale factor
Example ∆ABC ~ ∆JKL
1. Find the similarity Ratio of
1. Solve for the value of x.
1. Solve for m<J
Classwork
 Practice 8-2
Homework
 8-1 / 8-2 Worksheet