The sequence of rigid motions that will transform AGHI onto ASTU is:
Rotate AGHI 90 degrees clockwise around G.
Translate AGHI along TU until A reaches S.
Here are the steps to solve the problem:
Identify the key features:
Notice that both triangles are right-angled triangles.
AGHI has a right angle at G and ASTU has a right angle at A.
HI and TU are parallel lines.
Plan the transformation:
To move AGHI onto ASTU, we need to rotate and translate it.
Since HI and TU are parallel, we can rotate AGHI such that GH coincides with TU.
Then, we can translate AGHI along TU until A reaches S.
Perform the transformation:
Rotation: Rotate AGHI around G until GH coincides with TU. This can be done in 90 degrees clockwise or 270 degrees counter-clockwise.
Translation: Slide AGHI along TU until A reaches S.
Verify the solution:
After the rotation and translation, AGHI should completely overlap with ASTU.
Therefore, the sequence of rigid motions that will transform AGHI onto ASTU is:
Rotate AGHI 90 degrees clockwise around G.
Translate AGHI along TU until A reaches S.