1. 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)

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.

3. 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?

4. 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.

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

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

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

9. 9

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

11. 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

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

13. 13

14. 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

15. 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

16. 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