📐 Topic Summary
Rigid transformations (translations, rotations, and reflections) change the position or orientation of a figure without changing its size or shape. Dilations, on the other hand, change the size of a figure but not its shape. When a figure undergoes a sequence of rigid transformations followed by a dilation, the resulting figure is similar to the original. Similarity means that the figures have the same shape but can be different sizes.
🧩 Part A: Vocabulary
Match the terms with their definitions:
- Term: Translation
- Term: Rotation
- Term: Reflection
- Term: Dilation
- Term: Similarity
- Definition: A transformation that flips a figure over a line.
- Definition: A transformation that slides a figure without changing its orientation.
- Definition: A transformation that enlarges or reduces a figure proportionally.
- Definition: A transformation that turns a figure around a fixed point.
- Definition: When figures have the same shape but can be different sizes.
(Match the numbered terms with the lettered definitions.)
✍️ Part B: Fill in the Blanks
A _________ transformation preserves size and shape. A _________ changes the size of a figure. If two figures are similar, one can be mapped onto the other by a sequence of _________ transformations followed by a _________. The ratio of corresponding sides in similar figures is called the _________.
🤔 Part C: Critical Thinking
Explain, using examples, how you can determine if two triangles are similar after one has undergone a combination of a reflection, a translation, and a dilation. What properties of the triangles would you need to check?