# 9.1 Translations -Transformation: a change in the position, shape, or size of a geometric figure -Preimage: the original figure -Image: the resulting figure.

## Presentation on theme: "9.1 Translations -Transformation: a change in the position, shape, or size of a geometric figure -Preimage: the original figure -Image: the resulting figure."— Presentation transcript:

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: ReflectionTranslationRotationGlide 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:b 2. the ratio of their areas is a^2:b^2

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

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

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