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?
Lesson 6.2 A Table of Triangles
- Complete the tables for these three triangles:
- What do you notice about the values in the table for Triangle E but not for Triangles D and F?
- Complete the tables for these three more triangles:
- What do you notice about the values in the table for Triangle Q but not for Triangles P and R?
- What do Triangle E and Triangle Q have in common?
Lesson 6.3 Meet the Pythagorean Theorem
- Find the missing side lengths. Be prepared to explain your reasoning.
- 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.
Lesson 6 Practice Problems
- 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.
- 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.
- 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.
- Order the following expressions from least to greatest.
- Which is the best explanation for why -√10 is irrational?
- 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?
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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