Exploring Converse of Isosceles Triangle Theorem

In the GeoGebra Geometry app window below:
[size=150]1. Use the ANGLE WITH GIVEN SIZE tool [icon]/images/ggb/toolbar/mode_anglefixed.png[/icon] to construct an angle with side [math]\overline{AB}[/math] that measures [math]\alpha[/math] degrees and has a vertex at [i][b]A[/b][/i]. Notice [math]\alpha[/math] is the name of the slider you see. [br][br]2. After doing so, use the RAY tool [icon]/images/ggb/toolbar/mode_ray.png[/icon] to construct [b]ray[/b] [b][i]AB'[/i][/b]. [br][br]The silent video show how you can do both of these steps below. [/size]
Keep going: More directions appear below this applet.
[size=150]3. Use the ANGLE WITH GIVEN SIZE tool [icon]/images/ggb/toolbar/mode_anglefixed.png[/icon] to construct an angle with side [math]\overline{AB}[/math] that measures [math]\alpha[/math] degrees and has a vertex at [b][i]B[/i][/b]. After selecting this tool again, make sure to select [i][b]A[/b], [/i]then [b][i]B[/i],[/b] [b]in that order[/b], and make sure to rotate [math]\alpha[/math] degrees [b]clockwise. [/b][br][br]4. After doing so, use the RAY tool [icon]/images/ggb/toolbar/mode_ray.png[/icon] to construct [b]ray[/b] [b][i]BA'[/i][/b]. [br][/size]5. Now use the INTERSECT tool [icon]/images/ggb/toolbar/mode_intersect.png[/icon] to plot the point where the two rays (you constructed in steps (2) and (4) intersect. GeoGebra should label this point as[b] [i]C[/i][/b]. [br][br]6. Right click on each ray and uncheck SHOW OBJECT to hide it. Do the same for [b][i]B'[/i][/b] and [b][i]A'[/i][/b]. [br][br]7. Use the POLYGON tool [icon]/images/ggb/toolbar/mode_polygon.png[/icon] to construct [math]\Delta ABC[/math]. [br][br]8. Use the DISTANCE or LENGTH tool [icon]/images/ggb/toolbar/mode_distance.png[/icon] to measure the lengths of segments [math]\overline{AB}[/math] and [math]\overline{BC}[/math].
[size=150]What do you notice? (Be sure to select the MOVE tool [icon]/images/ggb/toolbar/mode_move.png[/icon] again and move points [b][i]A[/i][/b] and [b][i]B[/i][/b] around! [/size][br]
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Information: Exploring Converse of Isosceles Triangle Theorem