Proof of Pythagoras' Theorem.
Demonstrate Pythagoras’ Theorem.
Establish Pythagoras' Theorem.
Both figures shown here below are squares with a side length of a + b. Notice that the first figure is divided into two squares and two rectangles. The second figure is divided into a square and four right triangles with legs of lengths a and b. Let’s call the hypotenuse of these triangles c.
(1.) What is the total area of each figure?
(2.) Find the area of each of the 9 smaller regions shown the figures and label them.
(3.) Add up the area of the four regions in Figure F and set this expression equal to the sum of the areas of the five regions in Figure G. If you rewrite this equation using as few terms as possible, what do you have?
Demonstration of Pythagoras' Theorem.
Use the applet to explore the relationship between areas. Follow the directions below.
Try it again with different squares. Estimate the areas of the new Squares, A, B, and C.
Estimate the areas of these new Squares, A, B, and C.
(1.) Explain what you observe as you complete the activity.
(2.) What do you think we may be able to conclude?
Use the areas of the two identical squares to explain why 5² + 12² = 13².
Find the unknown side lengths in these right triangles.
Each number is between which two consecutive integers?