Question

the mapping of defg to defg is shown. which statements are true regarding 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:

Step1: Recall properties of rigid - transformation

In a rigid transformation (like translation, rotation, reflection), corresponding sides and angles are congruent. An isometric transformation is a rigid transformation where distances are preserved.

Step2: Analyze corresponding sides

For corresponding sides in a transformation of a polygon, the order of vertices matters. $\overline{EF}$ corresponds to $\overline{E'F'}$, so the statement " $\overline{EF}$ corresponds to $\overline{E'F'}$" is true. $\overline{FG}$ does not correspond to $\overline{GD}$, so the statement " $\overline{FG}$ corresponds to $\overline{GD}$" is false.

Step3: Analyze corresponding angles

In a rigid transformation, corresponding angles are congruent. So, $\angle EDG\cong\angle E'D'G'$ and $\angle DEF\cong\angle D'E'F'$.

Step4: Determine type of transformation

Since corresponding sides and angles are congruent, the transformation is isometric and a rigid transformation. So the statements "The transformation is not isometric" is false and "The transformation is a rigid transformation" is true.

Answer:

$\overline{EF}$ 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.