Question

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

Answer 1

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**.