Warm Up (Use the graph paper on your desk) Determine if the following sets of points form a parallelogram. 1. (–3, 0), (1, 4), (6, 0), (2, –4) 2. (1, 2), (–2, 2), (–2, 1), (1, –2) 3. (2, 3), (–3, 1), (1, –4), (6, –2)

Move the 9 to the first triangle. Problem of the Day How can you move just one number to a different triangle to make the sum of the numbers in each triangle equal? (Hint: There do not have to be exactly 3 numbers in each triangle.) Move the 9 to the first triangle.

Objective: Learn to transform plane figures using translations, rotations, and reflections. GSE: MGSE8.G.1- Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines. EQ: What is the relationship between reflections, rotations, and translations?

When you are on an amusement park ride, you are undergoing a transformation. A transformation is a change in a figure’s position or size. Translations, rotations, and reflections are types of transformations. The resulting figure, or image, of a translation, rotation, or reflection is congruent to the original figure. A translation slides a figure along a line without turning.

Additional Example 1: Graphing Translations on a Coordinate Plane Graph the translation of triangle ABC 2 units right and 3 units down. Rule Image

Check It Out: Example 1 Graph the translation of the quadrilateral ABCD 3 units down and 5 units left. Rule Image 7

A reflection flips a figure across a line to create a mirror image. 8

9

Additional Example 2: Graphing Reflections on a Coordinate Plane Graph the reflection of quadrilateral ABCD across the y-axis. Rule Image 10

Graph the reflection of triangle FGH across the x-axis. Check It Out: Example 2 Graph the reflection of triangle FGH across the x-axis. H’ G’ F’ Rule Image 11

A rotation turns a figure around a point, called the center of rotation. 12

13

Additional Example 3: Graphing Rotations on a Coordinate Plane Graph the rotation of triangle ABC 90 counterclockwise about the origin. A’ B’ C’ Rule Image 14

Graph the rotation of triangle XYZ 180 about the origin. Check It Out: Example 3 Graph the rotation of triangle XYZ 180 about the origin. Rule Image 15

Lesson Quiz Graph each transformation of triangle ABC. 1. translation 4 units down 2. reflection across the y-axis 3. rotation of 180 about the origin