Pythagorean Theorem, Revisited, Proof
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Lesson Plans and Worksheets for Grade 8
Lesson Plans and Worksheets for all Grades
More Lessons for Grade 8
Common Core For Grade 8
Examples, solutions, and videos to help Grade 8 students learn how to explain a proof of the Pythagorean Theorem using similar triangles and another proof using area.
• Students explain a proof of the Pythagorean Theorem.
Lesson 15 Classwork
Discussion
This discussion is an opportunity for students to practice explaining a proof of the Pythagorean Theorem using similar triangles.
• To prove the Pythagorean Theorem, a2 + b2 = c2, use a right triangle, shown below. Begin by drawing a segment from the right angle, perpendicular to side AB through point C. Label the intersection of the segments point D.
Discussion
• Now, let’s apply this knowledge to another proof of the Pythagorean Theorem. Compare the area of similar figures drawn from each side of a right triangle.
Pythagorean Theorem proof from similar right triangles
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Lesson Plans and Worksheets for Grade 8
Lesson Plans and Worksheets for all Grades
More Lessons for Grade 8
Common Core For Grade 8
Examples, solutions, and videos to help Grade 8 students learn how to explain a proof of the Pythagorean Theorem using similar triangles and another proof using area.
New York State Common Core Math Grade 8, Module 7, Lesson 15
Download Worksheets for Grade 8, Module 7, Lesson 15
Lesson 15 Student Outcomes
• Students know that the Pythagorean Theorem can be interpreted as a statement about the areas of similar geometric figures constructed on the sides of a right triangle.• Students explain a proof of the Pythagorean Theorem.
Lesson 15 Summary
The Pythagorean Theorem can be proven by showing that the sum of the areas of the squares constructed off of the legs of a right triangle is equal to the area of the square constructed off of the hypotenuse of the right triangle.Lesson 15 Classwork
Discussion
This discussion is an opportunity for students to practice explaining a proof of the Pythagorean Theorem using similar triangles.
• To prove the Pythagorean Theorem, a2 + b2 = c2, use a right triangle, shown below. Begin by drawing a segment from the right angle, perpendicular to side AB through point C. Label the intersection of the segments point D.
Discussion
• Now, let’s apply this knowledge to another proof of the Pythagorean Theorem. Compare the area of similar figures drawn from each side of a right triangle.
Pythagorean Theorem proof from similar right triangles
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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