Pythagorean Theorem, Revisited, Proof
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
Plans and Worksheets for Grade 8
Plans and Worksheets for all Grades
Lessons for Grade 8
Common Core For Grade 8
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
This discussion is an opportunity for students to practice explaining a proof of the Pythagorean Theorem using similar
• To prove the Pythagorean Theorem, a2
, 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.
• 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
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