Download Lesson 14: Similarity in Triangles

GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 14 M2
Name:______________________________
Date:___________
Lesson 14: Similarity in Triangles
Important notation: If 𝐴 and 𝐵 are similar, we write 𝐴~𝐵 where “~” denotes similarity.
Example 1
Using the reflexive property we say 𝐴~𝐴.
We said that for a figure 𝑨 in the plane, it must be true that 𝑨~𝑨.
Why is this true?
There are several different transformations that will map 𝑨 onto itself such as:

A rotation of 0° or a rotation of 360°.

A reflection of 𝐴 across a line and a reflection right back will achieve the same result.
l

A translation with a vector of length 0 also maps 𝐴 to 𝐴.

A dilation with scale factor 1 will map 𝐴 to 𝐴,
and any combination of these transformations will also map 𝐴 to 𝐴.
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Example 2
Using the symmetric property we say if 𝐴~𝐵, then 𝐵~𝐴.
We say that for figures 𝑨 & 𝑩 in the plane so that 𝑨~𝑩, it must be true that 𝑩~𝑨.
Why must this be true?
This condition must be true because for any composition of transformations that maps 𝐴 to
𝐵, there will be a composition of transformations that can undo the first composition.
For example, if:

A translation by vector ⃑⃑⃑⃑⃑
𝑋𝑌 maps 𝐴 to 𝐵, then the vector ⃑⃑⃑⃑⃑
𝑌𝑋 will undo the transformation
and map 𝐵 to 𝐴.

A rotation of 90° in the counterclockwise direction can be undone by a rotation of 90° in
the clockwise direction.

A dilation by a scale factor of 𝑟 = 2 can be undone with a dilation by a scale factor of
1
𝑟 = 2.

A reflection across a line can be undone by a reflection back across the same line.
Example 3
Using the transitive property we can say if 𝐴~𝐵 and 𝐵~𝐶, then 𝐴~𝐶.
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Example 4
The following triangles are similar.
a.
similarity statement
b.
Given the similarity statement, find the scale
factor for the ratio of the corresponding sides.
congruent angles
ABC ~ JLK
c.
corresponding sides
AB BC AC


JL LK JK
A  J
B  L
C  K
Exercise 1 and 2 For each pair of similar triangles:
a.
c.
1.
Write the similarity statement. b.
Name the congruent angles.
Write the correspondence between the sides. d. Determine the scale factor.
a.
similarity statement
b.
congruent angles
c.
corresponding sides
2. Given similar triangles ABC and DEF, complete a-d and find the missing side measures.
30
6
18
a.
similarity statement
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b.
congruent angles
c.
corresponding sides
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This work is licensed under a
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Name
Date
_____
Geometry M2L14 Similarity HW
Period ____________
1. Given similar triangles JKL and RST,
a.
Write the similarity statement
b.
Name the correspondence between all sides
and all angles.
c.
Find the measure of the missing angles.
2. Given similar triangles ABC and DEF,
a.
Write the similarity statement
10
b.
Name the correspondence between all sides and all angles.
c.
Find the scale factor.
d.
Find the measure of the missing sides.
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Date:
3
6
Similarity
3/31/16
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220
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.