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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: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