Date: 3/3 – 3/4/2015
Lesson number: #11/#12
Lesson Title: Similarity
Learning Target: Identify if triangles are similar, and calculate the missing side
IN:
length of a triangle using properites of simiar triangles.
Success Criteria:
before
after
Questions:
1.
2.
Notes:
I know what similar figures are.
I know how to use a scale factor or proportion to solve
for a missing side length.
1) How do you know if two figures are
similar?
2) Find r if |𝑂𝑃| = 7.5 and |𝑂𝑃′|= 10.5
Similarity:
Figures are similar if one figure is simply an enlargement or shrinking of the
other figure. The figures must be proportionate and be able map onto one
another through a sequence of dilations and congruences.
Similar figures have all equal angles and side lengths must be proportional.
Two ways to find if two figures are similar: 2
4
6
12
1. Check to see if the ratios of the 2. Find the proportional side lengths
corresponding sides are equal.
(scale factor)
2
1
4
- Set up a proportion with
=
=2
4
2
2
Corresponding sides.
or
6
1
12
- Set equal to each other and
=
=2
12
2
6
Cross multiply.
2
6
=
24=24, so they
4
12
Are similar
Two ways to calculate the measure of an unknown side when you are given a
pair of similar figure:
1) Calculate the scale factor, and then multiply by the scale factor.
- Set up the equation and solve for r
2) You can set up and solve a proportion.
- Use corresponding sides to set up proportions and solve for the
unknown side (x).
See the back of the notes for examples.
Summary: _________________________________________________________________________________________________
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Out:
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HW: _________________________
1) Exit ticket #11
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2) Exit ticket #12
3) IMB entry
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Example:
4.2
18.9
2.3
10.35
3.7
X
Using Scale Factor:
𝟐.𝟑𝒓
𝟐.𝟑
=
Using Proportions:
𝟏𝟎.𝟑𝟓
𝟒.𝟐𝒓
𝟐.𝟑
𝟒.𝟐
r = 4.5 cm
=
𝟏𝟖.𝟗
𝟒.𝟐
- Set up proportions with corresponding sides
r = 4.5 cm
2.3
10.35
=
3.7
2.3𝑥
𝑥
2.3
3.7(4.5) = x
X = 16.65 cm
=
38.295
2.3
x = 16.65 cm
4.2
18.9
=
3.7
4.2𝑥
𝑥
4.2
=
69.93
4.2
X = 16.65 cm