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More About Similar Triangles

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Examples, videos, and solutions to help Grade 8 students learn to present informal arguments as to whether or not two triangles are similar and how to find lengths of corresponding sides of similar triangles.

New York State Common Core Math Grade 8, Module 3, Lesson 11

Download Worksheets for Grade 8, Module 3, Lesson 11

Lesson 11 Student Outcomes

• Students present informal arguments as to whether or not two triangles are similar.
• Students practice finding lengths of corresponding sides of similar triangles.

Lesson 11 Summary

• Given just one pair of corresponding angles of a triangle as equal, use the side lengths along the given angle to determine if triangles are in fact similar.
• Given similar triangles, use the fact that ratios of corresponding sides are equal to find any missing measurements.

NYS Math Module 3 Grade 8 Lesson 11

Classwork
Example 1 & 2
Given the information provided, is △ ABC ∼ △ DEF?

Example 3
Given that △ ABC ∼ △ AB'C', could we determine the length of AB'?

Example 4
If we suppose XY is parallel to X'Y', can we use the information provided to determine if △ OXY ∼ △ OX'Y'?
Explain.

Example 5
Given the information provided, is △ OPQ ∼ △ Op'Q'?


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 line BC is parallel to line B'C'. With this information, can you say that △ ABC ∼ △ AB'C'. Explain.
c. Given that △ ABC ∼ △ AB'C' determine the length of AC'.
d. Given that △ ABC ∼ △ AB'C' determine the length of AB.

2. 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 A'C'.
d. Given that △ ABC ∼ △ A'B'C' determine the length of BC.

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.





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