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The figure KLMN is being rotated by 90°, which is a rigid transformation, the true statements are therefore;
(D) Figure RSTU is congruent to figure KLMN
(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
The given parameters are;
In KLMN, KN||LM
The transformation applied to figure KLMN = A 90° clockwise rotation about point P.
The image of KLMN following the rotation transformation is Figure RSTU.
Please find attached a drawing of the possible diagram in the question obtained from a similar question online.
The options from the question are;
(A) [tex] \overline{ST}[/tex] is parallel to [tex] \overline{RU}[/tex]
(B) [tex] \angle R[/tex] is the same measure as [tex] \angle N[/tex]
(C) [tex] \overline{RS} [/tex] is the same length as \overline{MN}
(D) Figure RSTU is congruent to figure KLMN
(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
A rotation transformation is a rigid transformation, therefore;
The distances between any two points on the pre–image is the same as the distance between corresponding points on the image, which gives;
Figure KLMN [tex] is congruent to [/tex] Figure RSTU
Figure KLMN [tex] \cong [/tex] Figure RSTU
According to the postulate, Corresponding Angles of Congruent Figures are Congruent, we have;
[tex] \angle T \cong \angle M[/tex]
Which gives;
[tex] \angle T[/tex] = [tex] \angle M[/tex]
[tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
The correct options are therefore;
(D) Figure RSTU is congruent to figure KLMN
(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
Learn more about rotation transformation in Euclidean geometry here:
https://brainly.com/question/4077402
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