Translate AGHJ by GS to superimpose GH on ST. Rotate around S until HJ aligns with TU (angle is HS-TU). Reflect across ST to map AGHJ onto ASTU.
The sequence of rigid motions that will definitely work is:
Translate AGHJ by vector GS. This will move AGHJ so that side GH coincides with side ST.
Rotate AGHJ' (the image of AGHJ after the first translation) around point S by an angle equal to the angle between HS and TU. This rotation will align side HJ with side TU.
Reflect AGHJ'' (the image of AGHJ after the first two transformations) over line ST.This reflection will map AGHJ'' onto ASTU.
Step-by-step explanation:
A rigid motion preserves the size and shape of a figure, and the problem asks for a sequence of such motions to map AGHJ onto ASTU.
The first step, translation, simply slides the figure without changing its orientation. We want to move AGHJ so that GH coincides with ST, and GS is the vector pointing from G to S.
After the first step, HJ is not aligned with TU. We need to rotate AGHJ' around point S by an angle that aligns HJ with TU. The angle between HS and TU is the angle needed for this rotation.
Finally, the reflection over line ST flips AGHJ'' across the line, resulting in ASTU.
Therefore, the sequence of translate-rotate-reflect is guaranteed to take AGHJ onto ASTU.