[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.92,0:00:05.88,Default,,0000,0000,0000,,Pythagoras theorem says that for\Nany right angle triangle area,
Dialogue: 0,0:00:05.88,0:00:12.33,Default,,0000,0000,0000,,see the area of the square of\Nthe hypotenuse equals A plus B.
Dialogue: 0,0:00:12.33,0:00:17.29,Default,,0000,0000,0000,,The some of the areas of the\Nother two squares.
Dialogue: 0,0:00:18.27,0:00:19.79,Default,,0000,0000,0000,,But how could we prove this?
Dialogue: 0,0:00:21.84,0:00:26.69,Default,,0000,0000,0000,,Let's start by making a second\Ncopy of the diagram.
Dialogue: 0,0:00:29.05,0:00:35.69,Default,,0000,0000,0000,,On the left hand copy will\Ndraw this square. It just
Dialogue: 0,0:00:35.69,0:00:39.32,Default,,0000,0000,0000,,surrounds the square on the\Nhypotenuse.
Dialogue: 0,0:00:40.49,0:00:44.03,Default,,0000,0000,0000,,And on the right-hand copy will\Ndraw this square.
Dialogue: 0,0:00:44.61,0:00:50.47,Default,,0000,0000,0000,,Again, it just surrounds the\Nsquares on the other two sides.
Dialogue: 0,0:00:53.65,0:01:00.07,Default,,0000,0000,0000,,Now these two knew squares we've\Ndrawn are both the same size.
Dialogue: 0,0:01:00.69,0:01:07.57,Default,,0000,0000,0000,,In each case, the side of the\Nnew square has length little A
Dialogue: 0,0:01:07.57,0:01:13.00,Default,,0000,0000,0000,,plus littleby. The sum of the\Nlength of the two shorter sides
Dialogue: 0,0:01:13.00,0:01:14.12,Default,,0000,0000,0000,,of the triangle.
Dialogue: 0,0:01:18.17,0:01:18.90,Default,,0000,0000,0000,,But now.
Dialogue: 0,0:01:20.23,0:01:24.15,Default,,0000,0000,0000,,Look at the areas of\Nthese two new squares.
Dialogue: 0,0:01:25.84,0:01:29.88,Default,,0000,0000,0000,,The one on the left is made up\Nof square, see.
Dialogue: 0,0:01:30.44,0:01:32.66,Default,,0000,0000,0000,,Plus 4 copies.
Dialogue: 0,0:01:33.40,0:01:34.38,Default,,0000,0000,0000,,Of the triangle.
Dialogue: 0,0:01:35.74,0:01:40.59,Default,,0000,0000,0000,,The one on the right is made up\Nof squares A&B.
Dialogue: 0,0:01:41.33,0:01:44.19,Default,,0000,0000,0000,,Plus 4 copies.
Dialogue: 0,0:01:45.24,0:01:46.23,Default,,0000,0000,0000,,Of the triangle.
Dialogue: 0,0:01:48.22,0:01:50.04,Default,,0000,0000,0000,,But they're both the same area.
Dialogue: 0,0:01:51.51,0:01:54.24,Default,,0000,0000,0000,,C plus four triangles.
Dialogue: 0,0:01:54.77,0:02:00.51,Default,,0000,0000,0000,,Equals area A plus area B\Nplus four triangles.
Dialogue: 0,0:02:01.43,0:02:07.26,Default,,0000,0000,0000,,So area C equals area A\Nplus area be.
Dialogue: 0,0:02:08.38,0:02:10.77,Default,,0000,0000,0000,,And that's Pythagoras theorem.