Geometry Chapter 9 Study Guide
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Geometry Chapter 9 Study Guide

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Questions and Answers

Describe this translation.

Translation is a geometric transformation that moves every point of a figure the same distance in a given direction.

What is a transformation?

A change in position, shape, or size of a geometric figure (i.e., reflection, translation, rotation, dilation).

Describe this translation.

Reflection is a transformation that flips a figure over a line, creating a mirror image.

What is rotation?

<p>This form of transformation always moves figures counterclockwise.</p> Signup and view all the answers

What is dilation?

<p>A transformation with center C and scale factor n (with n being greater than 0) resulting in enlargement or reduction of a figure.</p> Signup and view all the answers

What is an isometry?

<p>Another name for the following transformations: reflection, translation, and rotation.</p> Signup and view all the answers

What is a prime?

<p>The name for an asterisk following a letter (i.e., A').</p> Signup and view all the answers

What is the line of reflection?

<p>A transformation (over line r) following the rules that point A remains unchanged and line r is perpendicular to line BB'.</p> Signup and view all the answers

Describe reflection over the y-axis.

<p>A transformation that maps each point to its mirror image across the y-axis.</p> Signup and view all the answers

What is the center of rotation?

<p>A transformation where the image of point R is unchanged, and the angle of rotation is defined.</p> Signup and view all the answers

What is the angle of rotation?

<p>The positive number of degrees a figure rotates.</p> Signup and view all the answers

Steps to ____ ________:

<p>draw rotation</p> Signup and view all the answers

What is reflectional symmetry?

<p>A figure that has a reflection of itself in its own image.</p> Signup and view all the answers

What is rotational symmetry?

<p>A symmetry between a figure and its own image if rotation is 180 degrees or less.</p> Signup and view all the answers

What is point symmetry?

<p>A figure with 180-degree rotational symmetry; each segment joining a point and its image point passes through the center of rotation.</p> Signup and view all the answers

What is enlargement?

<p>Dilation with a scale factor value greater than 1.</p> Signup and view all the answers

What is reduction?

<p>Dilation with a scale factor value less than 1.</p> Signup and view all the answers

What is the equation for dilation on the coordinate plane?

<p>Point P (x,y) = Point P' (nx, ny).</p> Signup and view all the answers

What are parallel lines in terms of transformations?

<p>A composition of reflection with both lines perpendicular to two lines, along with translation.</p> Signup and view all the answers

What are intersecting lines in terms of transformations?

<p>A composition of reflection with center of rotation as the intersection point; the angle of rotation is twice the angle of the two lines.</p> Signup and view all the answers

What is glide reflection?

<p>A composition of translation (glide) and a reflection across a line parallel to the direction of the translation.</p> Signup and view all the answers

What does same orientation mean?

<p>Orientation caused by translations and rotations.</p> Signup and view all the answers

What does opposite orientation mean?

<p>Orientation caused by reflections and glide reflections.</p> Signup and view all the answers

Study Notes

Translation and Transformations

  • Translation refers to the movement of a geometric figure without changing its size or shape.
  • Transformation encompasses any change in position, shape, or size, including reflection, translation, rotation, and dilation.

Reflection

  • Reflection flips a figure over a line, creating a mirror image.
  • The line of reflection has specific rules guiding the transformation.

Rotation

  • Represents turning a figure around a point; typically measured in a counterclockwise direction.
  • The center of rotation is the point around which the figure is rotated.

Dilation

  • Involves resizing a figure, defined by a center point and a scale factor greater than zero.
  • Two key properties include: the center remains fixed, and for any other point, the image's distance from the center is multiplied by the scale factor.

Isometry

  • An isometry is a transformation that preserves distances, including reflections, translations, and rotations.

Symmetry

  • Reflectional symmetry exists when a figure can be divided into two mirror-image halves.
  • Rotational symmetry occurs when a figure can be rotated and still appear unchanged; applies to rotations of up to 180 degrees.
  • Point symmetry is a specific type of rotational symmetry where points are symmetric with respect to a center point.

Lines of Symmetry

  • A figure can have multiple lines of reflectional symmetry; each line divides the figure into mirror-image halves.
  • The number of lines of symmetry can determine the symmetry type of various figures.

Dilation Equations

  • Dilation on the coordinate plane can be represented as: Point P (x,y) = Point P' (nx, ny), where n is the scale factor.

Types of Dilation

  • Enlargement occurs when the scale factor is greater than 1, making the figure larger.
  • Reduction occurs when the scale factor is less than 1, making the figure smaller.

Line Intersections and Reflections

  • Parallel lines relate to reflections, defined by lines that do not intersect but are perpendicular to translation.
  • Intersecting lines involve reflections with a rotation centered at the intersection point, with the angle of rotation being double the angle between the lines.

Glide Reflection

  • A glide reflection combines a translation (glide) with a reflection across a line that is parallel to the direction of the translation.

Orientation

  • Translations and rotations maintain the same orientation of figures.
  • Reflections and glide reflections cause the figure to change to an opposite orientation.

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Description

This quiz focuses on key concepts from Geometry Chapter 9, covering translations, transformations, reflections, and rotations. Test your knowledge of geometric figures and their properties with these flashcards. Perfect for students preparing for exams or looking to reinforce their understanding of geometry.

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