Question

What are two different ways we could prove that two figures are congruent using translations? Why are we able to use translations to prove congruency between two figures

Answer 1

Two ways to prove congruency between two figures using translations are: using the definition of congruence and congruent corresponding parts. Translations preserve distances and angles, allowing us to slide a figure without changing its shape or size and proving congruency.

Step-by-step explanation:

Two different ways to prove that two figures are congruent using translations are:

1. Using the definition of congruence: Two figures are congruent if one figure can be obtained from the other by a combination of translations, rotations, and reflections.
2. Using congruent corresponding parts: If two figures have corresponding sides and angles that are congruent, and they can be superimposed by translations, then the figures are congruent.

We are able to use translations to prove congruency because translations preserve distances and angles. When we translate a figure, we are essentially sliding it without changing its shape or size. Therefore, if two figures are congruent after a translation, it means their corresponding sides and angles match up perfectly, proving their congruency.