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:

• Reflection only: A reflection can flip one triangle over a line to map it onto the other congruent triangle. Since the triangles are congruent (same shape and size), reflection (a rigid transformation) is valid.
• Rotation, then translation: Rotation (around a point) can re - orient one triangle, and then translation (sliding) can move it to the position of the other congruent triangle. Both rotation and translation are rigid transformations, and when combined, they can map one congruent triangle onto the other.
• Translation only: Looking at the orientation of the triangles (the way the vertices are arranged), a simple translation (sliding without rotation or reflection) cannot map one triangle onto the other as their orientations are different.
• Dilation, then translation: Dilation changes the size of a figure. Since the triangles are congruent (same size), dilation (a non - rigid transformation that changes size) is not allowed.
• Rotation then dilation: Again, dilation changes the size. Congruent triangles have the same size, so this combination is invalid.

Answer:

reflection only, rotation, then translation