Illustrative Mathematics Grade 8, Unit 8, Lesson 6: Finding Side Lengths of Triangles

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Illustrative Math
Grade 8

Lesson 6: Finding Side Lengths of Triangles

Let’s find triangle side lengths.

Illustrative Math Unit 8.8, Lesson 6 (printable worksheets)

Lesson 6 Summary

The following diagram explains the Pythagorean Theorem.

Lesson 6.1 Which One Doesn’t Belong: Triangles

Which triangle doesn’t belong?

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Lesson 6.2 A Table of Triangles

1. Complete the tables for these three triangles:
2. What do you notice about the values in the table for Triangle E but not for Triangles D and F?
3. Complete the tables for these three more triangles:
4. What do you notice about the values in the table for Triangle Q but not for Triangles P and R?
5. What do Triangle E and Triangle Q have in common?

Lesson 6.3 Meet the Pythagorean Theorem

1. Find the missing side lengths. Be prepared to explain your reasoning.
2. For which triangles does a² + b² = c²?

Are you ready for more?

If the four shaded triangles in the figure are congruent right triangles, does the inner quadrilateral have to be a square? Explain how you know.

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Lesson 6 Practice Problems

1. Here is a diagram of an acute triangle and three squares.
   Priya says the area of the large unmarked square is 26 square units because 9 + 17 = 26. Do you agree? Explain your reasoning.
2. m, p, and z represent the lengths of the three sides of this right triangle.
   Select all the equations that represent the relationship between m, p, and z.
3. The lengths of the three sides are given for several right triangles. For each, write an equation that expresses the relationship between the lengths of the three sides.
4. Order the following expressions from least to greatest.
5. Which is the best explanation for why -√10 is irrational?
6. A teacher tells her students she is just over 1 and 1/2 billion seconds old.
   a. Write her age in seconds using scientific notation.
   b. What is a more reasonable unit of measurement for this situation?
   c. How old is she when you use a more reasonable unit of measurement?

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