What you’ll learn
Understand preserved lengths and angles.
Key idea
Rigid motions preserve every pairwise distance and corresponding angle; preserving parallelism alone is insufficient.
All pairwise distances and angles are preserved in rigid motions; nontrivial stretch fails despite parallelism.
Worked example
Classify examples and non-examples for the concept 'Understand preserved lengths and angles'.
A right triangle has horizontal leg 2, vertical leg 7, and included angle 90 degrees. After a rigid translation, classify the claim that both corresponding leg lengths and their included angle remain unchanged. Compare with a proposed horizontal stretch factor 2.
- A rigid translation preserves corresponding lengths 2 and 7, and the included right angle of 90 degrees.
- A horizontal-only stretch (x,y)→(2x,y) changes leg 2 to 4, so it is not rigid even though horizontal lines remain parallel.
Answer: True — rigid translation preserves lengths 2,7 and the right angle; stretching is a different operation.
Quick Check
Classify examples and non-examples for the concept 'Understand preserved lengths and angles'.
A right triangle has horizontal leg 3, vertical leg 8, and included angle 90 degrees. After a rigid reflection, classify the claim that both corresponding leg lengths and their included angle remain unchanged. Compare with a proposed horizontal stretch factor 3.