[b]1) What do you notice?[br]2) What does it tell us?[/b]
1) The two small areas fit into the large area.[br][br]2) The sum of the areas two short side squares is equal to the area of the long side square.
Move the red and green sliders and watch what happens to the Blue area.
What do you notice if you add the red area and the green area together?
Red area + Green area = Blue area
If we denote the sides a, b, and c we can say:[br]Red area = a[math]^2[/math][br]Green area = b[math]^2[/math][br]Blue area = c[math]^2[/math][br][br]We found previously that:[br]Red area + Green area = Blue area[br][br]So;[br][math]a^2+b^2=c^2[/math] and this is [b]Pythagoras theorem[/b]
What kind of triangles are the three used above?
Pythagoras is used if you have [b]two[/b] sides of a [b]right angle triangle [/b]and you want to find the third side. [br][br][b]To find the longest side:[/b][br] [math]c=\sqrt{a^2+b^2}[/math][br][br][b]To find the short side:[/b][br][math]b=\sqrt{c^2-a^2}[/math][br]or[br][math]a=\sqrt{c^2-b^2}[/math]
If a = 4 and b =7,[br]what is c[math]^2[/math]
So then what would [b]c[/b] be?
If c = 6.25 and b = 5.34,[br]what is a[math]^2[/math]
So then what would [b]a[/b] be?
To practice finding the long side, complete this activity:[br]https://www.transum.org/software/SW/Starter_of_the_day/Students/Pythagoras_basics.asp?Level=1[br][br]To practice finding the short side, complete this activity:[br]https://www.transum.org/software/SW/Starter_of_the_day/Students/Pythagoras_basics.asp?Level=2