To show that triangle ABC can be transformed onto triangle ADEF using rigid motions, we need to perform a series of translations, rotations, and reflections.
Step 1: Translation
We can start by translating triangle ABC so that point A is placed on point D. This can be done by moving the entire triangle along vector AD. After the translation, point A will be coincident with point D, but the rest of the triangle will remain in the same orientation.
Step 2: Rotation
Now, we need to rotate the translated triangle about point D so that the side AD aligns with side DE. Let's call this rotated triangle A'B'C'. By choosing the appropriate angle of rotation, we can make side A'D coincide with side DE.
Step 3: Reflection
Finally, we need to perform a reflection across the line containing side DE to make side A'D coincide with side EF. This reflects triangle A'B'C' to triangle ADEF.
After performing these rigid motions (translation, rotation, and reflection), triangle ABC will be transformed onto triangle ADEF.
. In the triangles shown, let AB = DE, BC = EF
and CA = FD. Use Rigid Motions to show
ABC onto ADEF.
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