๐ Topic Summary
In geometry, rigid transformations are operations that move a figure without changing its size or shape. These transformations include translations (slides), rotations (turns), reflections (flips). Congruence proofs use these transformations to demonstrate that two figures are identical in size and shape. If a series of rigid transformations can map one figure onto another, the two figures are congruent. Understanding these concepts allows us to prove geometric relationships rigorously.
๐ Part A: Vocabulary
Match each term with its correct definition. Write the number of the definition next to the term.
| Term |
Definition |
| 1. Translation |
A. A transformation that flips a figure over a line. |
| 2. Rotation |
B. A transformation that slides a figure along a vector. |
| 3. Reflection |
C. Figures that have the same size and shape. |
| 4. Congruent |
D. A transformation that turns a figure about a point. |
| 5. Rigid Transformation |
E. A transformation that preserves size and shape. |
โ๏ธ Part B: Fill in the Blanks
Complete the paragraph below using the following words: congruent, orientation, distance, angle, transformation.
A rigid __________ is a way of moving a figure without changing its size or shape. These transformations preserve __________ and __________ measure. If two figures can be mapped onto each other using a series of rigid transformations, then the figures are __________. Rigid transformations do not change the size, but they can change the __________.
๐ค Part C: Critical Thinking
Explain, in your own words, how rigid transformations are used to prove that two triangles are congruent. Provide an example.