Unit 8
Finding Unknown Side Lengths
Pythagorean Theorem and Irrational Numbers
Lesson 8
Expressions and Equations
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Let’s find missing side lengths of right triangles.
Unit 8 ● Lesson 8
Learning
Goal
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Equations
Unit 8 ● Lesson 8 ● Activity 1
Which one doesn’t belong?
32 + b2 = 52
b2 = 52 – 32
32 + 52 = b2
32 + 42 = 52
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Warm-up: Which One Doesn’t Belong?
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Which One Is the Hypotenuse?
Unit 8 ● Lesson 8 ● Activity 2
Label all the hypotenuses with c.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Find the Missing Side Lengths
Unit 8 ● Lesson 8 ● Activity 3
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Find the Missing Side Lengths
Unit 8 ● Lesson 8 ● Activity 3
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Finding Unknown Side Lengths
Unit 8 ● Lesson 8
Draw a right triangle and label 2 of the 3 sides. Next, swap triangles with another student, solve for the missing length, then swap back to check your partner’s work.
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Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 8 ● Lesson 8
Learning
Targets
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Could be the Hypotenuse, Could be a Leg
Unit 8 ● Lesson 8 ● Activity 4
A right triangle has sides of length 3, 4, and x.
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Cool-down
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Pythagorean Theorem
Unit 8 ● Lesson 8
The Pythagorean Theorem describes the relationship between the side lengths of right triangles.
The diagram shows a right triangle with squares built on each side. If we add the areas of the two small squares, we get the area of the larger square.
The square of the hypotenuse is equal to the sum of the squares of the legs. This is written as a2 + b2 = c2.
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Glossary
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics
hypotenuse
Unit 8 ● Lesson 8
The hypotenuse is the side of a right triangle that is opposite the right angle. It is the longest side of a right triangle.
Here are some right triangles. Each hypotenuse is labeled.
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Glossary
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics
legs
Unit 8 ● Lesson 8
The legs of a right triangle are the sides that make the right angle.
Here are some right triangles. Each leg is labeled.
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Glossary
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics
This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.
All curriculum excerpts are under the following licenses:
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
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