Question

Alfred 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 blank rotations, reflections, and dilations translations, rotations, and reflection or translations, rotations, relfections, and dilations 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 blank the same measure or proportional, but unequal mesuars and corresponding sides have blank the same length or proportional but unequal lengths.

Answer 1

Here’s the completed argument with appropriate words and phrases filled in for each blank:

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 translations, rotations, and reflections 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 the same measure and corresponding sides have the same length.

This argument correctly explains the properties of congruent triangles.