Question

using transformations, justify why segments ad and cd are congruent. be specific: • translations are defined by starting and ending points • reflections are defined by lines • rotations are defined by centers and degrees of rotation you must submit a typed (type it) response, but you can use the \draw it\ to help with your explanation.

Explanation:

Step1: Identify possible transformation

If there is a line of symmetry (reflection) that passes through the mid - point of the line segment joining the mid - points of AD and CD and is perpendicular to the line segment joining their mid - points, then a reflection across this line will map segment AD onto segment CD.

Step2: Recall property of reflection

A reflection is a transformation that preserves distance. When a segment is reflected across a line of symmetry, the pre - image and the image segments are congruent. So, if a reflection can be found that maps AD to CD, then AD and CD are congruent.

Answer:

Segments AD and CD are congruent because there may exist a reflection across a line (defined by the appropriate geometric relationship between the segments) that maps segment AD onto segment CD, and reflections preserve segment lengths.