# Unit 1Transformations and Symmetry

## Lesson 1

### Learning Focus

Identify features of translations, rotations, and reflections.

### Lesson Summary

In this lesson, we explored how to perform rigid transformations using a variety of tools, such as tracing paper, rulers, protractors, and compasses; and using a variety of methods, such as counting the squares on the coordinate grid, drawing parallel lines, or folding an image over a line. We used these tools and strategies to identify key features of each of the transformations.

## Lesson 2

### Learning Focus

Recognize parallel and perpendicular lines in a coordinate plane.

### Lesson Summary

In this lesson, we learned criteria for determining if two lines in a coordinate plane are parallel or perpendicular. We also learned notation for indicating that lines are parallel or perpendicular in our written work.

## Lesson 3

### Learning Focus

Determine the rigid transformation that carries one image onto another.

### Lesson Summary

In this lesson, we identified the transformation, or sequence of transformations, that would carry one image onto another. We justified our claims by describing or showing the essential features of each transformation, such as the center of rotation or the line of reflection.

## Lesson 4

### Learning Focus

Write precise definitions of the rigid transformations.

### Lesson Summary

In this lesson, we wrote precise definitions of the three rigid-motion transformations: translation, rotation, and reflection, and explored why the words slide, turn, and flip were not adequate to use as definitions.

## Lesson 5

### Learning Focus

Identify transformations that carry an image onto itself.

### Lesson Summary

In this lesson, we explored line and rotational symmetry in different types of quadrilaterals. A figure is symmetric if a figure can be reflected across a line or rotated about a point onto itself. We found that diagonals and lines connecting the midpoints of opposite sides of a quadrilateral might be lines of symmetry, depending on the quadrilateral, and the point of intersection of the diagonals is the center of rotation for parallelograms, rectangles, rhombuses, and squares. The possible angles of rotation vary depending on the quadrilateral, but are always multiples of .

## Lesson 6

### Learning Focus

Find patterns of line and rotational symmetry in regular polygons.

### Lesson Summary

In this lesson, we examined lines of symmetry and rotational symmetry in regular polygons. We found that the number of lines of symmetry and the smallest angle of rotation could be related to the number of sides of the regular polygon.

## Lesson 7

### Learning Focus

Relate attributes of special quadrilaterals to symmetry.

### Lesson Summary

In this lesson, we used rigid transformations to examine properties of the sides, angles, and diagonals in parallelograms, rectangles, rhombuses, and squares. We learned that some quadrilaterals can be classified in terms of the properties they share with other quadrilaterals, such as congruent opposite sides or angles.