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NYS COMMON CORE MATHEMATICS CURRICULUM M2 Lesson 17 GEOMETRY
Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
S.109
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M2-TE-1.3.0-08.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar Classwork
Opening Exercise
1. The following right triangles are similar.
i. Find the unknown lengths of triangle .
ii. Find the unknown lengths of triangle .
Mini-Lesson
NYS COMMON CORE MATHEMATICS CURRICULUM M2 Lesson 17 GEOMETRY
Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
S.110
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M2-TE-1.3.0-08.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
SSS Example
2. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
NYS COMMON CORE MATHEMATICS CURRICULUM M2 Lesson 17 GEOMETRY
Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
S.111
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M2-TE-1.3.0-08.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
SAS Example
3. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
Exercises
4. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
5. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
NYS COMMON CORE MATHEMATICS CURRICULUM M2 Lesson 17 GEOMETRY
Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
S.112
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M2-TE-1.3.0-08.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
6. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
7. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
8. Given the diagram below, is on ̅̅̅̅ and is on ̅̅ ̅̅ , , , , and .
a. Show that .
b. Find and .
NYS COMMON CORE MATHEMATICS CURRICULUM M2 Lesson 17 GEOMETRY
Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
S.113
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M2-TE-1.3.0-08.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Problem Set
1. For parts (a) through (d) below, state which of the three triangles, if any, are similar and why.
a.
b.
c.
d.
NYS COMMON CORE MATHEMATICS CURRICULUM M2 Lesson 17 GEOMETRY
Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
S.114
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M2-TE-1.3.0-08.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
2. For each given pair of triangles, determine if the triangles are similar or not, and provide your reasoning. If the
triangles are similar, write a similarity statement relating the triangles.
a.
b.
c.
d.
NYS COMMON CORE MATHEMATICS CURRICULUM M2 Lesson 17 GEOMETRY
Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
S.115
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M2-TE-1.3.0-08.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
3. For each pair of similar triangles below, determine the unknown lengths of the sides labeled with letters.
a.
b.
4. Given that ̅̅ ̅̅ and ̅̅ ̅̅ intersect at and ̅̅ ̅̅ ̅̅ ̅̅ , show that .
NYS COMMON CORE MATHEMATICS CURRICULUM M2 Lesson 17 GEOMETRY
Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
S.116
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M2-TE-1.3.0-08.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
5. Given , , , and , show that .
6. Given the diagram below, is on ̅̅̅̅ and is on ̅̅ ̅̅ , , , , and .
a. Show that .
b. Find and .
7. One triangle has a angle, and a second triangle has a angle. Is it possible that the two triangles are similar?
Explain why or why not.
8. A right triangle has a leg that is , and another right triangle has a leg that is . Can you tell whether the
two triangles are similar? If so, explain why. If not, what other information would be needed to show they are
similar?
9. Given the diagram below, , , and , is there a pair of similar triangles? If so, write a similarity
statement, and explain why. If not, explain your reasoning.
