Geometry

1. Geometry Chapter 7 Benedict

2. Vocabulary Image- Figures can be reflected, rotated, or translated to produce new figures. Preimage- The original figure of an image. Transformation- Moving the pre-image onto the image.

3. Vocabulary Image- Figures can be reflected, rotated, or translated to produce new figures. Preimage- The original figure of an image. Transformation- Moving the pre-image onto the image.

4. Vocabulary Types of Transformations Translation

5. Practice Draw a figure below and use the three basic transformations to redraw your original shape.

6. Vocabulary Reflections- A transformation that uses a line that acts like a mirror with an image reflected in the line. Line of Reflection- the mirror line. Reflection Theorem- A reflection is isometry. Line of Symmetry- The figure can be mapped onto itself by a reflection in the line.

7. Practice Using your iPad or book; draw a picture of a reflection. Label the line of reflection and the line of symmetry.

8. Vocabulary Rotation- a transformation in which the figure is turned about a fixed point. Center of Rotation- the fixed point, about which the figure moves. Angle of Rotation- The point and its image for an angle. Rotation Theorem- A rotation is an isometry.

9. Practice Using your iPad or book, draw a picture of a rotation. Label the center and angle of rotation.

10. Vocabulary Rotational Symmetry- If the figure can be mapped onto itself by a rotation of 180° or less. Theorem 7.3- If lines k and m intersect at point P, then a reflection in k followed by a reflection in m is a rotation about point P.

11. Vocabulary Translation- A transformation that maps every to points P and Q in the plane to points P’ and Q’, so that the following properties are true. • PP’ = QQ’ • PP’ is parallel to QQ’ or PP’ and QQ’ are collinear Translation Theorem- A translation is an isometry.

12. Practice Using your iPad or book, draw a picture of a translation. Label the points and lines in the drawing.

13. Vocabulary Vector- A quantity that has both direction and magnitude, or size, and is represented by an arrow drawn between two points. Initial Point- Starting point of a vector. Terminal Point- Ending point of a vector. Component Form- A vector that combines vertical and horizontal components.

14. Practice Below draw a picture of a vector, label the initial and terminal point:

15. Vocabulary Glide Reflection- A transformation in which every point P is mapped onto a point P” by the following steps. • A translation maps P onto P’. • A reflection in a line k parallel to the direction of the translation maps P’ onto P”. Composition- When two or more transformations are combine to produce a single transformation.

16. Practice Using your iPad or book draw a picture of a glide reflection below:

17. Vocabulary Composition Theorem- The composition of two (or more) isometries is an isometry. Frieze Pattern/Border Pattern- A pattern that extends to the left and right in such a way that the pattern can be mapped onto itself by a horizontal translation.

18. Practice Draw the following Frieze Patterns below: • Translation • Translation about 180° rotation • Reflection in a horizontal line • Reflection in a vertical line • Horizontal glide reflection