Question

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

Explanation:

Step1: Recall congruent - transformation properties

Congruent triangles can be mapped onto each other by rigid - motions. Rigid motions include translation, rotation, and reflection. Dilation changes the size of a figure, and congruent triangles have the same size.

Step2: Analyze each option

• Reflection only: A reflection can map one congruent triangle onto another.
• Translation only: A translation can move one congruent triangle to the position of another.
• Dilation, then translation: Dilation is not a rigid - motion and changes the size, so this is incorrect for congruent triangles.
• Rotation, then translation: A rotation followed by a translation (both rigid - motions) can map one congruent triangle onto another.
• Rotation then dilation: Dilation changes the size, so this is incorrect for congruent triangles.

Answer:

reflection only, rotation, then translation