Question

name: mariah holland date: 9 - 5 - 25 introducing congruence (printable version) explore 1. how can you tell if a figure is a translation, reflection, or rotation of another figure? a translation slid it does not change shape 2. look at image 1 below. it is given that triangle def is congruent to triangle abc (δdef≅δabc) because δdef is a translation of δabc. if δdef is a translation of δabc, then what is true about the various sides and angles of the triangles? specifically, what parts of these two triangles are related, and how are they related? 3. in general, what can you say about the sides and angles of figures that are translations, reflections, or rotations of other figures? this work is licensed under a creative commons attribution - noncommercial sharealike 4.0 international license @2023 georgia department of education all rights reserved page 4 of 9

Explanation:

Step1: Recall congruence properties

In congruent figures (formed by translation, reflection or rotation), corresponding sides and angles are equal.

Step2: Identify corresponding parts for triangles

For $\triangle DEF$ and $\triangle ABC$ where $\triangle DEF$ is a translation of $\triangle ABC$, we have:
Corresponding sides: $\overline{DE}=\overline{AB}$, $\overline{EF}=\overline{BC}$, $\overline{DF}=\overline{AC}$.
Corresponding angles: $\angle D=\angle A$, $\angle E=\angle B$, $\angle F=\angle C$.

Step3: Generalize for all rigid - motions

Translations, reflections, and rotations are rigid - motions. In general, for figures that are translations, reflections, or rotations of other figures, corresponding sides are congruent (equal in length) and corresponding angles are congruent (equal in measure).

Answer:

1. For a translation, all points of the figure are moved the same distance in the same direction. For a reflection, the figure is flipped over a line of reflection. For a rotation, the figure is turned around a fixed point. In all these cases, the shape and size of the figure remain the same.
2. Corresponding sides: $\overline{DE}=\overline{AB}$, $\overline{EF}=\overline{BC}$, $\overline{DF}=\overline{AC}$; Corresponding angles: $\angle D=\angle A$, $\angle E=\angle B$, $\angle F=\angle C$.
3. Corresponding sides of figures formed by translations, reflections, or rotations are congruent, and corresponding angles are congruent.