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A Proof of the Pythagorean Theorem Lessons from the Math Zone © Copyright 2006, Don Link Permission Granted for Educational Use Only

base height 1.We start with half the red square, which has Area = ½ base x height 2.We move one vertex while maintaining the base & height, so that the area remains the same. This is called a SHEAR. 3.We rotate this triangle, which does not change its area. base height 4.We mark the base and height for this triangle. (Area of green square)+ (Area of red square)= Area of the blue square The Pythagorean Theorem:

base height 5.We now do a shear on this triangle, keeping the same area. Remember that this pink triangle is half the red square. Half the red square. (Area of green square)+ (Area of red square)= Area of the blue square The Pythagorean Theorem: 1.We start with half the red square, which has Area = ½ base x height 2.We move one vertex while maintaining the base & height, so that the area remains the same. This is called a SHEAR. 3.We rotate this triangle, which does not change its area. 4.We mark the base and height for this triangle.

(Area of green square)+ (Area of red square)= Area of the blue square The Pythagorean Theorem: 6.The other half of the red square has the same area as this pink triangle, so if we copy and rotate it, we get this. So, together these two pink triangles have the same area as the red square. 7.We now take half of the green square and transform it the same way. Half the red square. We end up with this triangle, which is half of the green square. Half the green square. 9.Together, they have they same area as the green square. So, we have shown that the red & green squares together have the same area as the blue square. Shear Rotate Shear 8.The other half of the green square would give us this.

(Area of green square)+ (Area of red square)= Area of the blue square The Pythagorean Theorem: 6.The other half of the red square has the same area as this pink triangle, so if we copy and rotate it, we get this. So, together these two pink triangles have the same area as the red square. 7.We now take half of the green square and transform it the same way. Half the red square. We end up with this triangle, which is half of the green square. Half the green square. 9.Together, they have they same area as the green square. So, we have shown that the red & green squares together have the same area as the blue square. We’ve PROVEN the Pythagorean Theorem! Shear Rotate Shear 8.The other half of the green square would give us this. We’ve Proven the Pythagorean Theorem