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 properties of congruent - triangle transformations

Congruent triangles have the same shape and size. Dilations change the size of a figure, so any transformation combination involving dilation cannot map congruent triangles onto each other.

Step2: Analyze each option

• Reflection only: A reflection flips a figure over a line. It can map one congruent triangle onto another.
• Translation only: A translation slides a figure. It can map one congruent triangle onto another.
• Rotation, then translation: A rotation turns a figure around a point, and a translation slides it. This combination can map one congruent triangle onto another.
• Rotation then dilation: Since dilation changes size, this cannot map congruent triangles onto each other.
• Dilation, then translation: Since dilation changes size, this cannot map congruent triangles onto each other.

Answer:

• Reflection only
• Translation only