Question

analyzing a transformation
the mapping of defg to defg is shown.
which statements are the transformation? check all that apply.
ef corresponds to ef
fg corresponds to gd
∠edg ≅ ∠edg
∠def ≅ ∠def
the transformation is not isometric.
the transformation is a rigid transformation.

Explanation:

To solve this, we analyze each statement based on rigid transformations (which preserve side lengths, angles, and are isometric):

1. $\boldsymbol{\overline{EF}}$ corresponds to $\boldsymbol{\overline{E'F'}}$: In a rigid transformation (like rotation/reflection/translation), corresponding sides of the pre - image and image are congruent and correspond. So this is true.
2. $\boldsymbol{\overline{FG}}$ corresponds to $\boldsymbol{\overline{G'D'}}$: $\overline{FG}$ should correspond to $\overline{F'G'}$ (not $\overline{G'D'}$) as per the order of the vertices in the pre - image ($DEFG$) and image ($D'E'F'G'$). So this is false.
3. $\boldsymbol{\angle EDG\cong\angle E'D'G'}$: Corresponding angles in a rigid transformation are congruent. $\angle EDG$ (in $DEFG$) and $\angle E'D'G'$ (in $D'E'F'G'$) are corresponding angles, so this is true.
4. $\boldsymbol{\angle DEF\cong\angle D'E'F'}$: Corresponding angles in a rigid transformation are congruent. $\angle DEF$ (in $DEFG$) and $\angle D'E'F'$ (in $D'E'F'G'$) are corresponding angles, so this is true.
5. $\boldsymbol{\text{The transformation is not isometric}}$: Rigid transformations are isometric (they preserve distance and shape). So this is false.
6. $\boldsymbol{\text{The transformation is a rigid transformation}}$: Since corresponding sides and angles are preserved (as seen from the congruence of corresponding parts), the transformation is rigid (preserves size and shape). So this is true.

Answer:

The correct statements are:

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