Create an interactive figure that allows your students to explore the angle sum in a triangle.

[table] [tr] [td]1.[/td] [td][icon]/images/ggb/toolbar/mode_polygon.png[/icon][/td] [td]Create a triangle [i]ABC[/i] with counter clockwise orientation.[/td][/tr] [tr] [td]2.[/td] [td][icon]/images/ggb/toolbar/mode_angle.png[/icon][/td] [td]Create the angles [i]α[/i], [i]β[/i] and [i]γ[/i] of triangle [i]ABC[/i].[/td][/tr] [tr] [td]3.[/td] [td][icon]/images/ggb/toolbar/mode_slider.png[/icon][/td] [td]Create a slider for angle [i]δ[/i] with Interval 0 ̊ to 180 ̊ and [i]Increment[/i] 10 ̊.[/td][/tr] [tr] [td]4.[/td] [td][icon]/images/ggb/toolbar/mode_slider.png[/icon][/td] [td]Create a slider for angle [i]ε[/i] with Interval 0 ̊ to 180 ̊ and [i]Increment[/i] 10 ̊.[/td][/tr] [tr] [td]5.[/td] [td][icon]/images/ggb/toolbar/mode_midpoint.png[/icon][/td] [td]Create midpoint [i]D[/i] of segment [i]AC[/i] and midpoint [i]E[/i] of segment [i]AB[/i].[/td][/tr] [tr] [td]6.[/td] [td][icon]/images/ggb/toolbar/mode_rotatebyangle.png[/icon][/td] [td]Rotate the triangle around point [i]D[/i] by angle [i]δ[/i] (setting [i]clockwise[/i]).[/td][/tr] [tr] [td]7.[/td] [td][icon]/images/ggb/toolbar/mode_rotatebyangle.png[/icon][/td] [td]Rotate the triangle around point [i]E[/i] by angle [i]ε[/i] (setting [i]counter clockwise[/i]).[/td][/tr] [tr] [td]8.[/td] [td][icon]/images/ggb/toolbar/mode_move.png[/icon][/td] [td]Move both sliders [i]δ[/i] and [i]ε[/i] to show 180 ̊.[/td][/tr] [/table]

1. What is happening to the sum of the interior angles as you move the the points around[br][br]2. What if you invert the angles, what happens to the sum of the exterior angles? [br][br]3. Does this work for every triangle you can think of? Experiment and consider the Extremes.[br][br]4. can you write a generalized equation to showcase the sum of the interior angles in a triangle?[br][br]5. Whilst trying out this applet i managed to create the following triangle, discuss with your partner how and why this can / cant be possible.[br][img width=398px;,height=301px;]https://lh7-rt.googleusercontent.com/slidesz/AGV_vUdUp9VHYBquJRLAuwEHPWGgZbLowVzjU-6Ow34CzTrDv33Axv2yx139orxiDsT_S87hn1k0fnleaStij2gF2NqsCfeGsK3XIyKhv5NcPL_a2VwyrfgPJVv3xkFOnhD0qQOhs9EM=s2048?key=oooap1K8sgg1hhfriOBWHQ[/img][br][br]