Question

the triangles are congruent by sss. which transformation(s) can be used to map one triangle onto the other? choose two correct answers. rotation then dilation reflection only rotation, then translation dilation, then translation translation only

Explanation:

• Congruent triangles have the same shape and size. Dilation changes the size of a figure, so any transformation involving dilation (rotation then dilation, dilation then translation) is incorrect as the triangles are congruent (same size).
• Reflection only: A reflection can flip one triangle over a line to map it onto the other congruent triangle.
• Rotation, then translation: A rotation can turn one triangle and then a translation (slide) can move it to map onto the other congruent triangle.
• Translation only: Just sliding (translation) may not be sufficient as the orientation (due to the non - parallel nature of the triangles in the given figure, inferred from the SSS congruence setup) might not match with a simple translation.

Answer:

B. reflection only, C. rotation, then translation