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This review covers fundamental concepts of transformations in geometry, including translations, reflections, rotations, and dilations. Key definitions such as preimage and image are outlined, alongside isometries and congruence. The review further explains composite transformations like glide reflections and symmetry types, including rotational, line, and translation symmetry. Real-world visual representations from Mrs. Liedell's quilt lab enhance understanding. This concise guide prepares students for the Chapter 8 exam by summarizing crucial ideas and vocabulary essential for mastering transformations.
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Chapter 8, Final Exam Review Nick DeFeudis
Transformations • Getting one set of points from another • When a rule is applied to points in the first set, resulting with a corresponding points in the second set • Definitions: • a transformation is a one-to-one correspondence between two sets of points • Preimage is the set of points before a transformation, and image is the product of the transformation
Translations • A translation is a slide, a movement in a single direction of all points • Are also the composite of two subsequent reflections
Reflections • A reflection is when the image created is the mirror image of the preimage • The creation of a mirror image is achieved by moving all points across a line of reflection at an equal distance in the image as in the preimage
Rotations • Center- point about which the figure is rotated • When a figure is moved about a single point, it is called a rotation
Rotations • Distances from the center point in the preimage don’t change in the image • A rotation is also the composite of two successive reflections through intersecting lines
Isometries and Congruence • Two figures are congruent if there is an isometry such that one figure is the image of the other • Dilations are not isometries because the shapes are not congruent after the transformation
Composite Transformations • An example of a composite transformation is a glide reflection • Glide reflections are the result of three reflections • They can also be considered a translation and a reflection
Dilations • A dilationis a transformation where the image and preimage are similar • When the image grows in size, it is an enlargement • When the image shrinks, it is a reduction
Rotation Symmetry • Rotational symmetry is when the figure looks exactly the same after a rotation of less than 360 degrees
Reflection (Line) Symmetry • A figure has line or reflection symmetry if and only if it coincides with its reflection image through the line
Translation Symmetry • A pattern has translation symmetry iff it coincides with a translation image • All points in one shape correspond with points in the other shape
Mrs. Liedell’s Quilt Lab • We saw visual representations of transformations in Mrs. Liedell’s quilts. • This unique way of presenting n-fold rotation, lines of reflection, translations and polygons helped to prepare us for the Chapter 8 test.
Summary/Key Ideas for Ch. 8 • Transformations (dilation, rotation, translation, reflection) • Kinds of symmetry (line, point, rotational) • Which transformations create similar and congruent figures • Vocab: preimage, image, etc.
