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

Slides:

Advertisements

Similar presentations

Chapter 1Foundations for Geometry Chapter 2Geometric Reasoning Chapter 3Parallel and Perpendicular Lines Chapter 4Triangle Congruence Chapter 5Properties.

Advertisements

Transformations Vocabulary.

Sasha Vasserman.  Two triangles are similar if two pairs of corresponding angles are congruent.

Geometry: Dilations. We have already discussed translations, reflections and rotations. Each of these transformations is an isometry, which means.

Chapter 9.1 Common Core G.CO.2, G.CO.4, & G.CO.6 – Represent transformations in the plane…describe transformations as functions that take points in the.

Transformations on the Coordinate Plane

Geometric Transformations:

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 9–3) NGSSS Then/Now New Vocabulary Key Concept: Glide Reflection Example 1: Graph a Glide Reflection.

Geometry Ch 12 Review Jeopardy Definitions Name the transformation Transform it!Potpourri Q $200 Q $400 Q $600 Q $800 Q $1000 Q $200 Q $400 Q $600 Q $800.

Rigid Motion in a Plane Reflection

9.6 Symmetry We are going to complete the tessellation first so get out your triangles.

Symmetry and Dilations

Geometric Transformations:

Using Rotations A rotation is a transformation in which a figure is turned about a fixed point. The fixed point is the center of rotation. Rays drawn from.

Isometries Page Isometry – A transformation in a plane that results in an image that is congruent to the original object. Which transformations.

Objectives Define and draw lines of symmetry Define and draw dilations.

Chapter 7 Transformations. Examples of symmetry Lines of Symmetry.

4.4 Congruence and Transformations

COMPOSITIONS OF TRANSFORMATIONS

Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that.

Chapter 12.  For each example, how would I get the first image to look like the second?

Transformations.

Section 7.3 Rigid Motion in a Plane Rotation. Bell Work 1.Using your notes, Reflect the figure in the y-axis. 2. Write all the coordinates for both the.

TRANSFORMATIONS Objective:  To identify isometries  To find reflection images of figures.

4-1 Congruence and transformations. SAT Problem of the day.

Lesson 14.5 Pre-AP Geometry

Dilations. Transformation – a change in position, size, or shape of a figure Preimage – the original figure in the transformation Image – the shape that.

Transformations, Symmetries, and Tilings

9-2 Reflections. Reflection Across a Line Reflection across a line (called the line of reflection) is a transformation that produces an image with a opposite.

2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Vocab 1 Vocab 2 Transformations CompositionsMiscellaneous.

4-7 Congruence Transformations. A transformation is an operation that maps an original geometric figure, the preimage, onto anew figure called the image.

Unit 10 Transformations. Lesson 10.1 Dilations Lesson 10.1 Objectives Define transformation (G3.1.1) Differentiate between types of transformations (G3.1.2)

Unit 3 Transformations This unit addresses transformations in the Coordinate Plane. It includes transformations, translations, dilations, reflections,

TransformationsTransformations. transformation One to One Mapping Preimage Point  Image Point A change of position or size of a figure. A  A´

Using Rotations A rotation is a transformation in which a figure is turned about a fixed point. The fixed point is the center of rotation. Rays drawn from.

OBJECTIVES: TO IDENTIFY ISOMETRIES TO FIND TRANSLATION IMAGES OF FIGURES Chapter 9 Section Translations.

Properties of Transformations. Translate Figures and Use Vectors Translation: moves every point of a figure the same distance in the same direction Image:

Pretest Please complete the pretest for this standard on your own. Try to remember all you can from our first discussion of this topic.

9-4 Compositions of Isometries. Isometry: a transformation that preserves distance or length (translations, reflections, rotations) There are 4 kinds.

 A transformation is an operation that moves or changes a geometric figure in some way to produce a new figure. The new figure is called the image. Another.

9.5 & 9.6 – Compositions of Transformations & Symmetry

Area Geometry Chapter 10.

Chapter 9 Vocab Review.

Section 12-4 Compositions of Reflections SPI 32D: determine whether the plane figure has been translated given a diagram.

12-7 Dilations.

9.4 Compositions of Transformations

Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.

Warm up Identify the transformation ∆RST → ∆XYZ.

Composition of Isometries & Dilations

Transformations Chapter 4.

If Q is not point P, then QP = Q 'P and m QPQ ' = x º.

Y. Davis Geometry Notes Chapter 9.

Introduction to Polygons - Part I

Warm-Up Graph the image of the polygon with vertices A(0,2), B(-2,-3), C(2, -3) after a dilation centered at the origin with a scale factor of 2.

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

7.3 Rotations Objectives: Identify rotations in a plane

Warm up Rotate P(-4, -4) 180 Rotate Q(-1, -3) 90 CCW

Warm up Rotate P(-4, -4) 180 Rotate Q(-1, -3) 90 CCW

10.1 Areas of parallelograms and triangles

TRANSFORMATION. TRANSFORMATION Foldable PRIME Original New IN MATH TERMS…. P -> P’

Drill: Monday, 9/28 Find the coordinates of the image of ∆ABC with vertices A(3, 4), B(–1, 4), and C(5, –2), after each reflection. 1. across the x-axis.

Unit 4 Transformations.

Invariance Under Transformations

Geometry Ch 12 Review Jeopardy

Warm up Identify the transformation ∆RST → ∆XYZ.

Dilations NOT an isometry.

Transformations Honors Geometry.

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