MOTION IN GEOMETRY: TRANSFORMATIONS

1. MOTION IN GEOMETRY:TRANSFORMATIONS 1.6 Geometry

2. CONGRUENCE • Figures that match exactly (SHAPE & SIZE) are said to be congruent

3. TRANSFORMATIONS • The movement of a figure in a plane from its original position, the preimage, to a new position, the image. • RIGID TRANSFORMATIONS • Transformations that do not change the size or shape of a figure.

4. Preimage The figure before you move it. Usually named with letters Example: A, B, AB… Image The figure after it has been moved Usually named with a letter and a prime symbol (apostrophe) Example: A’, B’, A’B’… Transformations

5. 3 Main Types of Transformations • TRANSLATIONS • ROTATIONS • REFLECTIONS

6. TRANSLATIONS • Every point of a figure moves in a straight line, and all points move the same distance and in the same direction.

7. EXAMPLES

8. ACTIVITY 1 • Translating an image

9. ROTATIONS • Every point of a figure moves around a given point known as the center of rotation. All points move the same angle measure.

10. EXAMPLES

11. EXAMPLES

12. ACTIVITY 2 • Rotating an image

13. REFLECTIONS • A line plays the role of a mirror, and every point in a geometric figure is “flipped” across the line.

15. EXAMPLES

16. EXAMPLES

17. ACTIVITY 3, PART 1 • The Reflection of a Point

18. If a point is reflected across a line, then the line is the ______________ ____________ of the segment that connects the point with its image.

19. ACTIVITY 3, PART 2 • The Reflection of a Triangle

20. If a triangle is reflected across a line, then the reflected image of the triangle is ____________ to the original triangle

21. Glide Reflection

22. Glide Reflection • A combination of a translation and a reflection.