Pythagorean Theorem and Volume

Lesson 9

Math

Unit 7

8th Grade

Lesson 9 of 16

Objective


Find missing side lengths involving right triangles and apply to area and perimeter problems.

Common Core Standards


Core Standards

  • 8.G.B.7 — Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Foundational Standards

  • 6.G.A.1
  • 7.G.B.6

Criteria for Success


  1. Use the Pythagorean Theorem to find the measures of missing legs and hypotenuses in right triangles. 
  2. Create or identify right triangles within other polygons in order to determine missing measurements using the Pythagorean Theorem (MP.7).

Tips for Teachers


In order to give approximate answers to the tenth of a unit, students may use calculators throughout this lesson. If time allows, students may also practice approximating square roots without calculators as a review of Lesson 2.

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Anchor Problems

25-30 minutes


Problem 1

Find the missing side length in each right triangle. Give an exact answer and an approximate answer to the nearest tenth of a unit. 

a.   

b.   

Guiding Questions

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Student Response

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Problem 2

Find the area of the isosceles triangle below. Give your answer to the nearest tenth of a square unit. 

Guiding Questions

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Student Response

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Problem 3

Find the perimeter of the triangle below. Give your answer to the nearest tenth of a unit. 

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


An isosceles trapezoid is composed of a square and two congruent triangles, as shown below. The area of the square is 16 units squared. Find the area of the trapezoid. 

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Solve real-world and mathematical problems using the Pythagorean Theorem (Part I).

Lesson 10
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Irrational Numbers and Square Roots

Topic B: Understanding and Applying the Pythagorean Theorem

Topic C: Volume and Cube Roots

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