Transformations and similarity unit test
1. What is a transformation in geometry?
A transformation in geometry is a function that maps one set of points to another set of points while preserving their relationships, such as distance and angle measures.
2. What are the three basic types of transformations?
The three basic types of transformations are translations, rotations, and reflections.
3. Describe a translation.
A translation is a transformation that moves every point of a figure a certain distance in a specified direction without changing its size or shape.
4. Explain the difference between a rigid transformation and a non-rigid transformation.
A rigid transformation, also known as an isometry, preserves the distances and angles between points, thus preserving the shape of the figure. A non-rigid transformation does not preserve the shape of the figure, as it may involve stretching, shrinking, or skewing.
5. What is similarity in geometry?
Two figures are considered similar if they have the same shape but not necessarily the same size.
6. How do you determine if two figures are similar?
Two figures are similar if their corresponding angles are congruent and their corresponding sides are proportional.
7. What is the ratio of similarity?
The ratio of similarity between two similar figures is the ratio of the lengths of corresponding sides.
8. How can you determine if two triangles are similar?
Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.
9. What is the similarity transformation?
A similarity transformation is a transformation that preserves the shape of a figure but may change its size. It includes dilation, rotation, reflection, and translation.
10. How are transformations and similarity related?
Transformations can help determine if two figures are similar by comparing their corresponding angles and side lengths. Similarity transformations preserve the shape of a figure while altering its size, making it easier to identify similarities between geometric objects.