In triangles FAD and DCE, translations of ABC, angle CAD equals angle ACB. Translations preserve corresponding angles, ensuring geometric congruence. The measure of CAD remains the same as ACB due to the congruent relationships established by the translation.
Triangles FAD and DCE are translations of triangle ABC, meaning they are congruent to ABC but may be positioned differently in space.
In a translation, corresponding angles have the same measure, and sides are equal in length. Angle CAD and angle ACB are corresponding angles in triangles FAD and ABC, respectively. As a result of the translation, these angles maintain the same measure.
The translation preserves the relationships between corresponding parts of the triangles, ensuring that angle CAD in FAD is congruent to angle ACB in ABC.
Therefore, the measure of angle CAD is equal to the measure of angle ACB due to the congruence established by the translation, demonstrating how the geometric properties of triangles are preserved under translations.