1. Pythagorean Theorem Proof 8th Math Presented by Mr. Laws
Geometry
Pythagorean Theorem Proof
8th Math
Presented by Mr. Laws
(a+ b)2 = C2 + 4ab/2

2. Standard
8.G.6 – Pythagorean theorem: Explain a proof of the Pythagorean Theorem and its converse.

3. Essential Question
How do I explain using a model, that the sum of the square of the legs is equal to the square of the hypotenuse in a right triangle?

4. Pythagorean Theorem Proof # 1b c
a2 + b2 = c2 C2
= 52 A2
= 25 B2

5. Pythagorean Theorem Proof # 2
Area of Big Square = Area of Small Square + 4 times the Area of the Triangles a b
Area of a Square is A = S2
A = (a+ b)2
A = C2 b a c c
Area of a Triangle is A = bh/2 a c c b
A = 4ab/2
(a+ b)2 = c2 + 4ab/2 b a

6. Pythagorean Theorem Proof # 2
Algebraic explanation of this Pythagorean Theorem Proof a b
(a+ b)2 = c2 + 4ab/2 b
(a + b) (a + b) = c2 + 4ab/2 a c c
a2 + ab + ab + b2 = c2 + 2ab
a2 + 2ab + b2 = c2 + 2ab a c c b
- 2ab
- 2ab
a2 + b2 = c2 b a

7. Other Pythagorean Theorem Proofs
Do you see how this proves the Pythagorean Theorem? Explain

8. Other Pythagorean Theorem Proofs
Do you see how this proves the Pythagorean Theorem? Explain

9. SUMMARY
Can you answer the essential question with confidence and a clear understanding of the lesson.
What are some key concepts you should remember about the Pythagorean Theorem Proofs
Is there more you need to learn about this lesson?

10. ___________________ = ___________________ + __________________
Name:_______________________________
Student CW/Activity
Complete the diagram and fill in the blanks below:. .
Write an equation and prove the Pythagorean Theorem
Area of the large square = area of the small square + area of the 4 triangles
___________________ = ___________________ + __________________
Multiply
Simplify