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lfred correctly explains a correspondence between two triangles. Select a word or phrase for each blank to complete Alfred's argument. 1. Suppose triangle ABC is congruent to triangle DEF. 2. Then there is a series of rigid motions that maps triangle ABC onto triangle DEF. (3 points) 3. Any of a triangle preserves the distances between every pair of corresponding points in the triangle. 4. Therefore, if two triangles are congruent, then corresponding angles have and corresponding sides have

1 answer

To complete Alfred's argument, we can fill in the blanks as follows:

  1. Suppose triangle ABC is congruent to triangle DEF.
  2. Then there is a series of rigid motions that maps triangle ABC onto triangle DEF.
  3. Any rigid motion of a triangle preserves the distances between every pair of corresponding points in the triangle.
  4. Therefore, if two triangles are congruent, then corresponding angles have equal measures and corresponding sides have equal lengths.

So, the filled-in argument reads:

  1. Suppose triangle ABC is congruent to triangle DEF.
  2. Then there is a series of rigid motions that maps triangle ABC onto triangle DEF.
  3. Any rigid motion of a triangle preserves the distances between every pair of corresponding points in the triangle.
  4. Therefore, if two triangles are congruent, then corresponding angles have equal measures and corresponding sides have equal lengths.