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:

1. Reflection Only: Since the triangles are congruent (SSS) and symmetric with respect to the line through \( K \) and \( L \), a reflection over this line can map one triangle onto the other.
2. Rotation, then Translation: First, rotate one triangle around a point (e.g., the midpoint of \( JL \) or \( KM \)) to align its orientation, then translate it to match the position of the other triangle.

• Translation Only: The triangles are not in a position where only translation (sliding without rotation/reflection) can map them, as their orientations differ.
• Dilation, then Translation or Rotation then Dilation: Dilation changes size, but the triangles are congruent (same size), so dilation is invalid.

Answer:

A. reflection only
D. rotation, then translation