1. Is [math]\angle[/math]BAC congruent to [math]\angle[/math]EDF?
2. Is [math]\angle[/math]ABC congruent to [math]\angle[/math]DEF?
3. Segment AB corresponds to segment DE. Segment BC corresponds to segment EF. Segment AC corresponds to segment DF. Are the corresponding segments in the same proportion?
4. [math]\angle[/math]ABC corresponds to [math]\angle[/math]DEF. [math]\angle[/math]ACB corresponds to [math]\angle[/math]DFE. [math]\angle[/math]BAC corresponds to [math]\angle[/math]EDF. Are the corresponding angles congruent?
5. Repeat questions 1-4 but, this time, change the value of the sliders. (You do not need to erase your answers in questions 1-4.) Did your answers to the Yes or No questions change?
The triangles you have made in Plane 1 exhibit AA similarity. The AA (angle-angle) similarity theorem states that for any pair of triangles: [i][b]if two pairs of corresponding angles are congruent, then the pair of triangles are similar[/b][/i][i][b].[/b] [/i]This means that with just the conditions said in the previous statement, the shapes already exhibit the properties of total side-proportionality and total angle-congruence.