Almost-Twin Triangles (Triangle Similarity)
Plane 1
Assessment for Combination 1
1. Is BAC congruent to EDF?
2. Is ABC congruent to 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. ABC corresponds to DEF. ACB corresponds to DFE. BAC corresponds to 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?
AA Similarity Theorem
The triangles you have made in Plane 1 exhibit AA similarity. The AA (angle-angle) similarity theorem states that for any pair of triangles: if two pairs of corresponding angles are congruent, then the pair of triangles are similar. 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.