[color=#000000]In the applet below, you'll find two triangles.  [br][br][/color][color=#000000]In the [/color][color=#38761d][b]green triangle[/b][/color][color=#000000], the [b]black angle is the included angle between sides [/b][/color][b][i][color=#000000]a[/color][/i][color=#000000] and [/color][i][color=#000000]b[/color][/i][/b][color=#000000].  [/color][br][color=#000000]In the [/color][b][color=#ff00ff]pink triangle[/color][/b][color=#000000], the [b]black angle is the included angle between sides [i]k[sub]a[/sub][/i] and [i]k[sub]b[/sub][/i][/b].  [br][br]The [b]corresponding sides[/b] a -> ka and b -> kb are in the[b] same proportion[/b] "k".[br][br][/color][math]\frac{k_b}{b}=k[/math] and [math]\frac{k_a}{a}=k[/math][br][br][color=#000000]The [b]black angle[/b] in the [/color][color=#38761d][b]green triangle[/b][/color] [b][color=#000000]is congruent to[/color][/b][color=#000000] the [/color][b][color=#000000]black angle[/color][/b][color=#000000] in the [/color][b][color=#ff00ff]pink triangle[/color][/b][color=#000000]. [/color][br][br][br][br][br][b][color=#ff0000]INTERACT[/color][/b] with the applet below for a few minutes. [color=#000000]As you do, be sure to move the locations of the [/color][color=#38761d][b]green triangle's[/b][/color][color=#000000] [b]BIG BLACK VERTICES[/b] and the location of the [b]BIG X[/b].[br][/color][color=#000000]You can also adjust the value of [/color][i][color=#000000]k[/color][/i][color=#000000] by using the slider or by entering a value between 0 & 1. [/color][color=#000000] [br][/color][color=#000000] [/color]

[b][color=#ff0000][size=150][u]QUESTION: [/u][/size]From your observations, what can you conclude about the two triangles?  Why can you conclude this? Clearly justify your response!  [/color][/b]