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# Geom 7point1

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### Geom 7point1

1. 1. Transformations <ul><li>Objectives: </li></ul><ul><li>Identify the 3 basic rigid transformations </li></ul><ul><li>Reflections </li></ul><ul><li>Rotations </li></ul><ul><li>Translations </li></ul>
2. 2. Transformation <ul><li>Figures can be reflected, rotated, or translated to form a new figure. </li></ul><ul><li>The new figure is called the image. </li></ul><ul><li>The original figure is called the preimage. </li></ul><ul><li>The operation that moves the preimage onto the image is called a transformation . </li></ul>
3. 3. Reflection <ul><li>Reflection in a line </li></ul>
4. 4. Rotation <ul><li>Rotation about a point </li></ul>
5. 5. Translation <ul><li>Moving it over </li></ul>
6. 6. Labeling Transformations <ul><li>When we name an image, we take the corresponding point of the preimage and add the prime symbol (‘). </li></ul><ul><li>For example, if the preimage is A, the image is A’ </li></ul>
7. 7. Naming Transformations <ul><li>What kind of transformation is this? </li></ul><ul><li>A reflection in the y-axis </li></ul><ul><li>Are the 2 triangles congruent? </li></ul><ul><li>yes </li></ul>
8. 8. Naming Transformations <ul><li>We can say that ∆ABC  ∆A’B’C’ </li></ul>A A B B C C
9. 9. Isometry <ul><li>An isometry is a transformation that preserves </li></ul><ul><ul><li>Length </li></ul></ul><ul><ul><li>Angle measures </li></ul></ul><ul><ul><li>Parallel lines </li></ul></ul><ul><ul><li>Distances between points </li></ul></ul>A A B B C C
10. 10. Does this transformation appear to be isometric? A A B B C C
11. 11. Does this transformation appear to be isometric?
12. 12. Does this transformation appear to be isometric?
13. 13. Does this transformation appear to be isometric?
14. 14. Preserving length & angle measurement P X Y Q R Z 58˚ <ul><li>In this diagram, ∆PQR is mapped onto ∆XYZ </li></ul><ul><li>∆ PQR --> ∆XYZ is an isometry </li></ul><ul><li>What is the length of YZ? </li></ul><ul><li>What is the measure of angle X? </li></ul>3
15. 15. Try some <ul><li>P. 398 - Example 4 </li></ul><ul><ul><li>How are pieces 1 & 2 related? </li></ul></ul><ul><ul><li>How are pieces 3 & 4 related? </li></ul></ul><ul><li>P. 399 - #5, #6, #7 </li></ul><ul><li>P. 401 #42, #42, #43 </li></ul>
16. 16. Homework: 2 worksheets