Download LESSON 15:THE AACRITERION FOR SIMILAR TRIANGLES

GEOMETRY
Lesson 15
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:__________________________________
M2
Date:_______________
LESSON 15: THE AA CRITERION FOR SIMILAR TRIANGLES

IMPORTANT NOTATION: IF 𝑨 AND 𝑩 ARE SIMILAR, WE WRITE 𝑨~𝑩 WHERE “~” DENOTES SIMILARITY.
THEOREM: Two triangles with two pairs of equal corresponding angles are similar.
This is known as the AA criterion for similarity.
We know that similar figures have equal corresponding angle measures. We also know if two
angles in one triangle are equal in measure to two corresponding angles in another triangle, then
it must be the case that the third corresponding angles in each triangle must also be of equal
measure.
ex.
40⁰
40⁰
35⁰
0⁰
35⁰
0⁰
In Exercises 1–4, practice using the AA criterion to determine if two triangles are similar and
then determine unknown side lengths and/or angle measures of the triangles.
1.
Are the triangles shown below similar? Explain. If the triangles are similar,
identify any missing angle and side length measures.
28
20
3
8
6
44.42°
57.12°
78.46°
7
Lesson 15:
Date:
57.12°
The Angle-Angle (AA) Criterion for Two Triangles to be Similar
4/1/16
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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2.
Are the triangles shown below similar? Explain. If the triangles are similar,
identify any missing angle and side length measures.
3.
The triangles shown below are similar. Use what you know about similar triangles to
find the missing side lengths 𝒙 and 𝒚.
4.
The triangles shown below are similar. Write an explanation to a student, Claudia,
of how to find the lengths of 𝒙 and 𝒚.
Lesson 15:
Date:
The Angle-Angle (AA) Criterion for Two Triangles to be Similar
4/1/16
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
230
Name
Date
Geometry L.15 AA Similarity
HW
Period:______________
1.
a.
b.
2.
a.
b.
Lesson 15:
Date:
The Angle-Angle (AA) Criterion for Two Triangles to be Similar
4/1/16
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
231
3.
a.
b.
c.
d.
Lesson 15:
Date:
The Angle-Angle (AA) Criterion for Two Triangles to be Similar
4/1/16
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
232