Question

is cdef similar to lmno? justify your answer.
yes, because a translation left 7 units and down 10 units maps cdef onto lmno.
yes, because a rotation 180° around the origin maps cdef onto lmno.
no, because ∠c and ∠l do not have the same measure.

Explanation:

Step1: Analyze translation and rotation properties

Translation and rotation are rigid transformations. Rigid transformations preserve shape and size (i.e., congruence). Similarity requires a proportional scaling (along with possible rotation, translation, reflection). If a translation or rotation maps one figure to another, the figures are congruent (a special case of similarity with scale factor \(k = 1\)). But we need to check if the general similarity conditions (angle - angle - angle or side - side - side similarity ratios) are met in a non - congruent sense (if applicable). However, looking at the options:

• A translation (first option) and a rotation (second option) would imply congruence (since they are rigid motions). But the problem is about similarity. Also, if we assume the standard properties of similarity (for polygons, corresponding angles are equal and corresponding sides are in proportion).
• For two polygons to be similar, all corresponding angles must be equal. If \(\angle C\) and \(\angle L\) (assuming \(C\) is a vertex of \(CDEF\) and \(L\) is a vertex of \(LMNO\)) do not have the same measure, then the polygons do not satisfy the angle - angle - angle (for quadrilaterals, sum of interior angles is \(360^{\circ}\), but individual angles must match) similarity criterion.

Answer:

No, because \(\angle C\) and \(\angle L\) do not have the same measure.