Pythagorean Theorem step by step a c b Picture This!

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Presentation transcript:

Pythagorean Theorem step by step a c b Picture This!

start with a right triangle

a label the sides c b

a construct a square on each side c b

find the center of the square on a by drawing its diagonals a c b

Then copy side c a c b

and slide it over−parallel to side c a c b to the center of the square on a

Draw the perpendicular bisector a c b

The 2 perpendicular bisectors at the center divide the square into a c b 4 equal parts

The length of each arm radiating out from the center is equal to half of side c c c 2 c 2 c 2 c 2

Sliding side c along the base to the center of the square c also makes a parallelogram

So side b of the triangle is equal to the long side of the quadrilateral. c b b plus the shortest side of the quadrilateral

slide the 4 quadrilaterals over to the big square a c b

The outsides fit because each one is half of side c. a c b

The insides fit because each one equals side b plus the short side a c b

The square on b fills the space in the middle of the square on c so we’re done! a c b

a c b for right triangles... We had to cut up the square on side a to do it, but we proved that

a c b the sum of the squares on the legs

a c b is equal to the square on the hypotenuse

a c b a2a2 +b2b2 = c2c2