Question

the triangles are congruent by sss and hl. which transformation(s) can be used to map △rst onto △vwx? reflection only translation only reflection, then translation rotation, then translation

Explanation:

Step1: Analyze triangle orientation

Observe $\triangle RST$ and $\triangle VWX$: the right angle of $\triangle RST$ is at the top-left, while the right angle of $\triangle VWX$ is at the bottom-right. A reflection will flip the triangle to match the orientation of the target triangle.

Step2: Analyze position alignment

After reflection, the triangle will have the same orientation as $\triangle VWX$, but it will still be in a different position. A translation (slide) will move the reflected triangle to exactly overlap $\triangle VWX$.

Step3: Evaluate other options

• Reflection only: Leaves the triangle in a mirrored position, not overlapping $\triangle VWX$.
• Translation only: Cannot fix the reversed orientation of the triangles.
• Rotation then translation: Rotation would not correctly align the right angle and side orientations to match $\triangle VWX$.

Answer:

reflection, then translation