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com B Unit $4$ Test $\newline$ Which of the following are examples of isometries? Pick all that apply ( $1$ point) $\newline$ (i) parallelogram $EFGH \rightarrow$ parallelogram $XWVU$ $\newline$ (ii) hexagon $CDEFGH \Rightarrow$ hexagon $TUVWKY$ $\newline$ (iii) triangle $\triangle EFO = \triangle VWU$

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Write equations of parabolas in vertex form using properties

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Q. *com B Unit

4

Test*

\newline

Which of the following are examples of isometries? Pick all that apply (

1

point)

\newline

(i) parallelogram

EFGH \rightarrow

parallelogram

XWVU

\newline

(ii) hexagon

CDEFGH \Rightarrow

hexagon

TUVWKY

\newline

(iii) triangle

\triangle EFO = \triangle VWU

Isometries Definition: Isometries are transformations that preserve distances and angles, meaning the pre-image and image are congruent. Examples of isometries include translations, rotations, reflections, and glide reflections. We need to determine if the given transformations are isometries.
Parallelogram Transformation: ( $1$ ) Parallelogram $EFGH \rightarrow$ parallelogram $XWVU$ . If $EFGH$ is transformed into $XWVU$ and all corresponding sides and angles remain equal, then this is an example of an isometry. However, without specific information about how the transformation was performed or if the sides and angles are indeed congruent, we cannot definitively say this is an isometry.
Hexagon Transformation: (ii) Hexagon $CDEFGH \rightarrow$ hexagon $TUVWKY$ . Similar to the parallelogram, if the hexagon $CDEFGH$ is transformed into hexagon $TUVWKY$ and all corresponding sides and angles remain equal, then this transformation is an isometry. Again, without specific information about the transformation or confirmation of congruency, we cannot definitively say this is an isometry.
Triangle Transformation: (iii) Triangle $EFO \rightarrow$ triangle $VWU$ . If triangle $EFO$ is transformed into triangle $VWU$ and they are congruent (all corresponding sides and angles are equal), then this transformation is an isometry. As with the previous shapes, without specific information about the transformation or confirmation of congruency, we cannot definitively say this is an isometry.

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