Curriculum / Math / 8th Grade / Unit 7: Pythagorean Theorem and Volume / Lesson 8
Math
Unit 7
8th Grade
Lesson 8 of 16
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Lesson Notes
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Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle.
The core standards covered in this lesson
8.G.B.6 — Explain a proof of the Pythagorean Theorem and its converse.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Read the examples of statements and their converses shown below.
a. Which of the converse statements are true?
b. The Pythagorean Theorem states: If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse, or $${a^2+b^2=c^2}$$. What is the converse statement of the Pythagorean Theorem?
c. Do you think the converse of the Pythagorean Theorem is true?
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For each triangle below, determine if the triangle is a right triangle. If it is, label the right angle in the diagram. (Figures not drawn to scale.)
The triangle below is not a right triangle.
Change the measurement of one of the side lengths to create a right triangle. Label the right angle in the diagram.
A set of suggested resources or problem types that teachers can turn into a 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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Is the triangle shown below a right triangle? Justify your answer. If it is, label the right angle in the diagram.
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
Find missing side lengths involving right triangles and apply to area and perimeter problems.
Topic A: Irrational Numbers and Square Roots
Define, evaluate, and estimate square roots.
Standards
8.EE.A.2
Understand that some numbers, including $${\sqrt{2}}$$, are irrational. Approximate the value of irrational numbers.
8.NS.A.18.NS.A.2
Locate irrational values approximately on a number line. Compare values of irrational numbers.
8.NS.A.2
Represent rational numbers as decimal expansions.
8.NS.A.1
Represent decimal expansions as rational numbers in fraction form.
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Topic B: Understanding and Applying the Pythagorean Theorem
Understand the Pythagorean Theorem as a relationship between the side lengths in a right triangle.
8.G.B.6
Understand a proof of the Pythagorean Theorem.
8.G.B.7
Solve real-world and mathematical problems using the Pythagorean Theorem (Part I).
Solve real-world and mathematical problems using the Pythagorean Theorem (Part II).
Find the distance between points in the coordinate plane using the Pythagorean Theorem.
8.G.B.8
Topic C: Volume and Cube Roots
Define and evaluate cube roots. Solve equations in the form $${x^2=p}$$ and $${x^3=p}$$.
8.EE.A.28.NS.A.2
Solve real-world and mathematical problems involving the volume of cylinders and cones.
8.G.C.9
Solve real-world and mathematical problems involving the volume of spheres.
Solve real-world problems involving multiple three-dimensional shapes, in particular, cylinders, cones, and spheres.
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