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Almost-Twin Triangles (Triangle Similarity)

Author:Sarah Walton, Alexis Sparks
Topic:Angles

Plane 1

Assessment for Combination 1

1. Is BAC congruent to EDF?

Select all that apply
  • A
  • B
Check my answer (3)

2. Is ABC congruent to DEF?

Select all that apply
  • A
  • B
Check my answer (3)

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?

Select all that apply
  • A
  • B
Check my answer (3)

4. ABC corresponds to DEF. ACB corresponds to DFE. BAC corresponds to EDF. Are the corresponding angles congruent?

Select all that apply
  • A
  • B
Check my answer (3)

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?

Select all that apply
  • A
  • B
Check my answer (3)

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.

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