Question

for each transformation in the table below, indicate which properties are true by placing a check mark in every appropriate box. transformation
translation
reflection
rotation
dilation the image and preimage are congruent the image and preimage are similar but not congruent lengths of segments are preserved measures of angles are preserved

Explanation:

Step1: Recall transformation properties

Translation, rotation and reflection are rigid - motions. Dilation is a non - rigid motion.

Step2: Analyze congruence and similarity

Translation, rotation and reflection produce congruent images (same shape and size), so for translation, rotation and reflection: the image and pre - image are congruent. Dilation changes the size, so the image and pre - image are similar but not congruent for dilation.

Step3: Analyze length preservation

Lengths of segments are preserved in translation, rotation and reflection (rigid motions). In dilation, lengths of segments are not preserved (scaled by a factor).

Step4: Analyze angle preservation

Measures of angles are preserved in all of translation, rotation, reflection and dilation.

Transformation	The image and pre - image are congruent	The image and pre - image are similar but not congruent	Lengths of segments are preserved	Measures of angles are preserved
Rotation	√		√	√
Reflection	√		√	√
Translation	√		√	√

Answer:

Transformation	The image and pre - image are congruent	The image and pre - image are similar but not congruent	Lengths of segments are preserved	Measures of angles are preserved
Rotation	√		√	√
Reflection	√		√	√
Translation	√		√	√