Question

the mapping of defg to defg is shown. which statements are true regarding the transformation? check all that apply. □ \\( \overline{ef} \\) corresponds to \\( \overline{ef} \\). □ \\( \overline{fg} \\) corresponds to \\( \overline{gd} \\). □ \\( \angle edg \cong \angle edg \\) □ \\( \angle def \cong \angle def \\) □ the transformation is not isometric. □ the transformation is a rigid transformation.

Explanation:

1. For $\overline{EF}$ and $\overline{E'F'}$: In a transformation mapping, corresponding sides are mapped from the original figure to the image. Since $E$ maps to $E'$ and $F$ maps to $F'$, $\overline{EF}$ corresponds to $\overline{E'F'}$, so this statement is true.
2. For $\overline{FG}$ and $\overline{G'D'}$: $F$ maps to $F'$, $G$ maps to $G'$, so $\overline{FG}$ should correspond to $\overline{F'G'}$, not $\overline{G'D'}$. So this statement is false.
3. For $\angle EDG$ and $\angle E'D'G'$: Corresponding angles in a rigid transformation (like rotation/reflection/translation) are congruent. Since the transformation is rigid (as we'll see later), $\angle EDG\cong\angle E'D'G'$, so this statement is true.
4. For $\angle DEF$ and $\angle D'E'F'$: Corresponding angles in a rigid transformation are congruent. $D$ maps to $D'$, $E$ to $E'$, $F$ to $F'$, so $\angle DEF\cong\angle D'E'F'$, this statement is true.
5. For "The transformation is not isometric": Isometric transformations preserve distance (and thus angles, area, etc.). Rigid transformations (rotation, reflection, translation) are isometric. Since the figure's sides and angles are preserved (corresponding sides/angles congruent), the transformation is isometric, so this statement is false.
6. For "The transformation is a rigid transformation": Rigid transformations preserve the shape and size (distance, angle measure). Since corresponding sides are congruent (marked with same tick marks) and corresponding angles are congruent (marked with same arc marks), the transformation (likely a rotation or reflection) is rigid, so this statement is true.

Answer:

• $\boldsymbol{\overline{EF}}$ corresponds to $\boldsymbol{\overline{E'F'}}$.
• $\boldsymbol{\angle EDG \cong \angle E'D'G'}$
• $\boldsymbol{\angle DEF \cong \angle D'E'F'}$
• $\boldsymbol{\text{The transformation is a rigid transformation.}}$