NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 11
8•3
Lesson 11: More About Similar Triangles
Classwork
Exercises
1.
In the diagram below, you have △ 𝐴𝐵𝐶 and △ 𝐴𝐵′ 𝐶 ′. Use this information to answer parts (a)–(d).
a.
Based on the information given, is △ 𝐴𝐵𝐶~ △ 𝐴𝐵′ 𝐶 ′ ? Explain.
b.
Assume the line containing 𝐵𝐶 is parallel to the line containing 𝐵′𝐶′. With this information, can you say that △
𝐴𝐵𝐶~ △ 𝐴𝐵′ 𝐶 ′ ? Explain.
c.
Given that △ 𝐴𝐵𝐶~ △ 𝐴𝐵′ 𝐶 ′ , determine the length of side ̅̅̅̅̅
𝐴𝐶′.
d.
Given that △ 𝐴𝐵𝐶~ △ 𝐴𝐵′ 𝐶 ′ , determine the length of side ̅̅̅̅
𝐴𝐵 .
Lesson 11:
More About Similar Triangles
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M3-TE-1.3.0-08.2015
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
2.
Lesson 11
8•3
In the diagram below, you have △ 𝐴𝐵𝐶 and △ 𝐴′𝐵′ 𝐶 ′ . Use this information to answer parts (a)–(c).
a.
Based on the information given, is △ 𝐴𝐵𝐶~ △ 𝐴′𝐵′ 𝐶 ′ ? Explain.
b.
Given that △ 𝐴𝐵𝐶~ △ 𝐴′𝐵′ 𝐶 ′ , determine the length of side ̅̅̅̅̅
𝐴′𝐶′.
c.
Given that △ 𝐴𝐵𝐶~ △ 𝐴′𝐵′ 𝐶 ′ , determine the length of side ̅̅̅̅
𝐵𝐶 .
Lesson 11:
More About Similar Triangles
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M3-TE-1.3.0-08.2015
S.57
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
3.
Lesson 11
8•3
In the diagram below, you have △ 𝐴𝐵𝐶 and △ 𝐴′𝐵′ 𝐶 ′ . Use this information to answer the question below.
Based on the information given, is △ 𝐴𝐵𝐶~ △ 𝐴′𝐵′ 𝐶 ′ ? Explain.
Lesson 11:
More About Similar Triangles
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M3-TE-1.3.0-08.2015
S.58
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
8•3
Lesson Summary
Given just one pair of corresponding angles of a triangle as equal, use the side lengths along the given angle to
determine if the triangles are in fact similar.
|∠𝐴| = |∠𝐷| and
1
2
=
3
6
= 𝑟; therefore, △
𝐴𝐵𝐶~ △ 𝐷𝐸𝐹.
Given similar triangles, use the fact that ratios of corresponding sides are equal to find any missing measurements.
Problem Set
1.
In the diagram below, you have △ 𝐴𝐵𝐶 and △ 𝐴′𝐵′ 𝐶 ′. Use this information to answer parts (a)–(b).
a.
b.
Based on the information given, is △ 𝐴𝐵𝐶~ △ 𝐴′𝐵 ′ 𝐶 ′ ? Explain.
̅̅̅̅ is 4.3. What is the length of side ̅̅̅̅̅̅
Assume the length of side 𝐴𝐶
𝐴′ 𝐶 ′ ?
Lesson 11:
More About Similar Triangles
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M3-TE-1.3.0-08.2015
S.59
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
2.
3.
Lesson 11
8•3
In the diagram below, you have △ 𝐴𝐵𝐶 and △ 𝐴𝐵′ 𝐶 ′. Use this information to answer parts (a)–(d).
a.
Based on the information given, is △ 𝐴𝐵𝐶~ △ 𝐴𝐵′ 𝐶 ′ ? Explain.
b.
c.
Assume the line containing ̅̅̅̅
𝐵𝐶 is parallel to the line containing ̅̅̅̅̅̅
𝐵′𝐶′. With this information, can you say that △
′ ′
𝐴𝐵𝐶~ △ 𝐴𝐵 𝐶 ? Explain.
Given that △ 𝐴𝐵𝐶~ △ 𝐴𝐵′ 𝐶 ′ , determine the length of side ̅̅̅̅̅
𝐴𝐶 ′ .
d.
Given that △ 𝐴𝐵𝐶~ △ 𝐴𝐵′ 𝐶 ′ , determine the length of side ̅̅̅̅̅
𝐴𝐵′ .
In the diagram below, you have △ 𝐴𝐵𝐶 and △ 𝐴′𝐵′ 𝐶 ′. Use this information to answer parts (a)–(c).
b.
Based on the information given, is △ 𝐴𝐵𝐶~ △ 𝐴′𝐵′ 𝐶 ′ ? Explain.
Given that △ 𝐴𝐵𝐶~ △ 𝐴′𝐵′ 𝐶 ′ , determine the length of side ̅̅̅̅̅̅
𝐵′ 𝐶 ′ .
c.
Given that △ 𝐴𝐵𝐶~ △ 𝐴′𝐵′ 𝐶 ′ , determine the length of side ̅̅̅̅
𝐴𝐶 .
a.
Lesson 11:
More About Similar Triangles
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M3-TE-1.3.0-08.2015
S.60
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
4.
Lesson 11
8•3
In the diagram below, you have △ 𝐴𝐵𝐶 and △ 𝐴𝐵′ 𝐶 ′. Use this information to answer the question below.
Based on the information given, is △ 𝐴𝐵𝐶~ △ 𝐴𝐵′ 𝐶 ′ ? Explain.
5.
In the diagram below, you have △ 𝐴𝐵𝐶 and △ 𝐴′𝐵′ 𝐶 ′ . Use this information to answer parts (a)–(b).
a.
b.
Based on the information given, is △ 𝐴𝐵𝐶~ △ 𝐴′𝐵 ′ 𝐶 ′ ? Explain.
′ 𝐵′ .
̅̅̅̅̅̅
Given that △ 𝐴𝐵𝐶~ △ 𝐴′𝐵′ 𝐶 ′ , determine the length of side 𝐴
Lesson 11:
More About Similar Triangles
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M3-TE-1.3.0-08.2015
S.61
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.