Introduction
In the previous lessons, you have studied all about angles, as well as learned about parallel lines and angles formed by parallel lines cut by a transversal. In the coming lessons, you will learn about transformations and how figures are moved around.
- The first type of transformation you will learn is a translation.
- Reflections and rotations are also transformations, but you will learn about them later.
To introduce the definition of a translation, use the Translation Exploration activity from GeoGebra to complete the 8.02 Exploring Translations task.
Explore Activity text version | Open Explore Activity in a new tab
Following successful completion of this lesson, students will be able to...
- Verify experimentally the properties of translations
- Understand that a two-dimensional figure is congruent to another if the second can be obtained by a translation
- Describe the effects of translations on two-dimensional figures
- Understand that a two-dimensional figure is similar to another if the second can be obtained by a translation
- Use graph paper and/or software to draw and identify a sequence of transformations that will carry a given figure onto another
Essential Questions
- How can you change a figure’s position with changing its size and shape?
- How can we identify the transformation of a figure in a coordinate plane?
- After performing a sequence of transformations on a figure, will the resulting image have the same size and shape?
Enduring Understandings
- Shape and area can be conserved during mathematical transformations.
- The symmetry of polygons can be described in rotations and reflections.
- We can use x and y coordinates to calculate translations in the coordinate plane.
- Rotations, reflections and translations are examples that preserve angles and distances.
- Geometric transformations are functional relationships.
The above objectives correspond with the Alabama Course of Study: Geometry standard: 21, 21a, 22, 22a, 22b