clear
unit 17.75
snap off
gridstyle grid off axes  off unit 1.0 1
style label  on coord  off filled  off font 12 color 0 0 0 fillcolor 128 128 128
let A=[point [-9.0, -4.0]]
Style A visible on 
let B=[point [9.915492957746478, -4.112676056338028]]
Style B visible on 
let C=[point [2.028169014084507, 6.929577464788732]]
Style C visible on 
let segAB=[seg [A B]   ]
Style segAB visible on label off unit 2 color 255 0 0 
let segBC=[seg [B C]   ]
Style segBC visible on label off unit 2 color 255 0 0 
let segAC=[seg [A C]   ]
Style segAC visible on label off unit 2 color 255 0 0 
let D=[pton segAB 0.33879374534623974]
Style D visible on unit 2 
let line1=[Perpendicular D segAB]
Style line1 visible off label off 
let G=[Intersection segAC line1]
Style G visible on unit 2 
let line3=[Perpendicular G line1]
Style line3 visible off label off 
let H=[Intersection segBC line3]
Style H visible on unit 3 
let line4=[Perpendicular H line3]
Style line4 visible off label off 
let I=[Intersection segAB line4]
Style I visible on unit 2 
let segDG=[seg [D G]   ]
Style segDG visible on label off unit 3 color 0 51 255 
let segGH=[seg [G H]   ]
Style segGH visible on label off unit 3 color 0 51 255 
let segHI=[seg [H I]   ]
Style segHI visible on label off unit 3 color 0 51 255 
let segDI=[seg [D I]   ]
Style segDI visible on label off unit 3 color 0 0 255 
let E=[point [-4.563380281690141, 15.605633802816902]]
label E "From Polya's How to Solve It problem 19, page 23. For any triangle is it always possible to draw a square inside the triangle with  one side on the triangle base"
Style E visible on 
let F=[point [-4.563380281690141, 14.47887323943662]]
label F "and each of the other corners of the square are on the other sides of the triangle?"
Style F visible on 
let J=[point [-4.450704225352113, 13.23943661971831]]
label J "Drag D along AB to see rectangles with this type of property. Drag C around to create different triangles."
Style J visible on 
let K=[point [-4.450704225352113, 11.830985915492958]]
label K "How would you answer Polya's question and how would you reason about your answer?"
Style K visible on 
let L=[point [-4.169014084507042, 10.140845070422536]]
label L "What happens if you drag C far to the left or the right?"
Style L visible on