9.1 Translations

-Transformation: a change in the position, shape, or size of a geometric figure

-Preimage: the original figure

-Image: the resulting figure

-Isometry: when the original figure and resulting figure are congruent

-Composition: a combination of 2 or more transformations

9.1 Translations

-Translation: an isometry that maps all points of a figure the same distance in the same direction

9.2 Reflections

-Reflection: an isometry in which a figure and its image have opposite orientations

9.3 Rotations

-Rotation: need the center of rotation (point), the angle of rotation (positive degree measure), and if the rotation is clockwise or counterclockwise

Symmetry-Symmetry: if there is an isometry that maps a figure onto itself

- Reflectional Symmetry: if the isometry is the reflection of a plane figure

-Rotational Symmetry: if the isometry of a preimage is the image after a rotation of 180*

9.4 Compositions of reflections

-Theorem 9.1: A translation or rotation is a composition of 2 reflections

-Theorem 9.2: A composition of reflections across 2 parallel lines is a translation

-Theorem 9.3: A composition of reflections across 2 intersecting lines is a rotation

-Theorem 9.4: In a plane, 1 of 2 congruent figures can be mapped onto the other by a composition of at most 3 reflections

-Glide Reflection: the composition of a translation and a reflection across a line parallel to the direction of translation

-Theorem 9.5: there are only 4 isometries: Reflection Translation Rotation Glide Reflection

9.6 Dilation

-Dilation: a transformation whose preimage and image are similar

-Enlargement: a dilation if the scale factor is greater than 1

-Reduction: a dilation if the scale factor is less than 1

Tesselations

-Tesselation: a repeating pattern of figures that completely covers a plane, without gaps or overlaps. You can make tesselations with translations, rotations, and reflections

-Theorem 9.6: every triangle tessellates

-Theorem 9.7: every quadrilateral tessellates

10.1 Areas of parallelograms and triangles

10.2 Areas of trapezoids, rhombuses, and kites

10.3 areas of Regular polygons

-Area of regular Polygon:

10.4 Perimeters and areas of similar figures

-Theorem 10.7: If the similarity ratio of two similar figures is a:b then…

1. the ratio of their perimeters is a:b2. the ratio of their areas is a^2:b^2

10.5 Trigonometry and areaThe area of any triangle given SAS is…

10.6 – 10.7 Area of Circles, area of sectors, and arc length