Subjects geometry

Rigid Motions 37D60D

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1. **Problem statement:** We need to describe a sequence of rigid motions (translations, rotations, reflections) that maps figure ABCDEFG onto figure JKLMNPQ, given that they are congruent. 2. **Understanding rigid motions:** Rigid motions preserve distances and angles. They include translations (sliding), rotations (turning), and reflections (flipping). 3. **Step 1: Identify corresponding points:** From the problem, vertex J corresponds to B, and vertex Q corresponds to C. This helps us understand how the figures align. 4. **Step 2: Translation:** Translate figure ABCDEFG so that point B coincides with point J. This moves the entire figure without rotation or reflection. 5. **Step 3: Rotation:** Rotate the translated figure around point J so that the segment BC aligns with segment JQ. The angle of rotation is the angle between segments BC and JQ. 6. **Step 4: Reflection (if needed):** If after translation and rotation the figure does not coincide exactly, reflect the figure across the line through JQ to match the orientation of JKLMNPQ. 7. **Summary:** The sequence is: translate ABCDEFG so B maps to J, rotate around J to align BC with JQ, then reflect if necessary to match the orientation. This sequence of rigid motions maps figure ABCDEFG onto figure JKLMNPQ exactly.