Question

is triangle def congruent to triangle xyz?
oa. yes, triangle def was reflected across its side df and translated 8 units to the left to create triangle xyz
ob. yes, triangle def was reflected across its side fe and translated 2 units to the left to create triangle xyz
oc. yes, triangle def was reflected across its side fe and translated 8 units to the left to create triangle xyz
od. no, triangle def is not congruent to triangle xyz

Explanation:

Step1: Recall congruence and transformation properties

Congruent triangles have the same shape and size. Transformations like reflection and translation do not change the size and shape of a figure.

Step2: Analyze the options

• Option A: If triangle DEF was reflected across its side DF and translated 8 units to the left, the size and shape of the triangle would remain the same. So triangle DEF would be congruent to triangle XYZ.
• Option B: Translating 2 units is not enough to map DEF to XYZ as per the grid - based visual (assuming standard grid - unit - based congruence determination from the figure's position).
• Option C: Reflecting across FE is not the correct axis of reflection (assuming the figure's orientation) to get congruence.
• Option D: Since reflection and translation (when done correctly as in Option A) preserve congruence, this option is wrong.

Answer:

A. Yes, Triangle DEF was reflected across its side DF and translated 8 units to the left to create triangle XYZ