1. Proving Pythagoras By Marshall Knauf Bhaskara’s Second Proof of the Pythagorean Theorem

2. Step One Start with a right triangle Legs= a, b Hypotenuse= c a c b

3. Step Two We label the triangle with lines a, b, and c Points A, B, and C Lines x, y Altitude h A B C M a c b xy h

4. Step Three Proof by similar triangles ABM~ CAB ACM~ CAB Angle Angle similarity A B C M a c b xy h

5. Step 4 Angle B = Angle BAM x/b=b/c Multiply both sides by b/c xc=b^2 A B C M a c b xy h

6. Step 5 Angle CAB = Angle AMC y/a = a/c Multiply both sides by ac yc = a^2 A B C M a c b xy h

7. Step 6 Add results yc+xc = a^2+b^2 c(x+y) = a^2+b^2 c^2 = a^2+b^2 Thus, Pythagoras is proven A B C M a c b xy h

8. Credits Everything Marshall Knauf Thank You www.jwilson.coe.uga.eduwww.jwilson.coe.uga.edu for the proof

9. One More Thing May 5 th Vote Marshall Knauf ASB Activities Commissioner