1. 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 plane as inputs and give other points as outputs… Objective – To identify rigid motions. To find translation images of figures.

2. Chapter 9.1 Notes Transformations ReflectionRotationTranslation Preimage – is the object you start with Image – is the object you end up with once you do the transformation Isometry – is a transformation that preserves lengths

3. Rigid Motion – is a transformation that preserves distance and angle measure. Translation – is a transformation that maps all points of a figure the same distance in the same direction A translation pushes a figure around

4. Composition of Transformations is a combination of two or more transformations. In a composition, you perform each transformation on the image of the preceding transformation.

5. Chapter 9.2 Common Core G.CO.5, G.CO.2, G.CO.4, & G.CO.6 – Given a geometric figure and a rotation, reflection, or translation, draw the tarnsformed figure…Specify a sequence of transformations that will carry a given figure onto another. Objective – To find reflection images of figures.

6. Chapter 9.2 Notes Reflection – A reflection is an isometry When we reflect, we reflect over a line Line of symmetry – is a line that when you reflect the figure over the line it is mapped onto itself Ex

7. Chapter 9.3 Common Core G.CO.4, G.CO.2, & G.CO.6 – Develop definitions of rotations…in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Objective – To draw and identify rotation images of figures.

8. Chapter 9.3 Notes Rotation – rotation is an isometry When rotating, you rotate about a point.

9. Chapter 9.4 Common Core G.CO.5 & G.CO.6 – Specify a sequence of transformations that will carry a given figure onto another. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motions on a given figure… Objectives – To find compositions of isometries, including glide reflections. To classify isometries.

10. Chapter 9.4 Notes Composition Thm – the composition of two (or more) isometries is an isometry Glide Reflection – is a composition where you first do a translation and then do a reflection.

11. Chapter 9.5 Common Core G.CO.7, G.CO.6, & G.CO.8 – Use the definition of congruence in terms of rigid motions to show that two triangles are congruent… Objectives – To identify congruence transformations. To prove triangle congruence using ismoetries.

12. Chapter 9.5 Notes Two figures are congruent if and only if there is a sequence of one or more rigid motions that maps one figure onto the other. Because compositions of rigid motions take figures to congruent figures, that are also called congruence transformations

13. Chapter 9.6 Common Core G.SRT.1a, G.SRT.1b, G.CO.2, & G.SRT.2 - A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. Objective – To understand dilation images of figures

14. Chapter 9.6 Notes Dilations 1) reduction – which means it is getting smaller A A’ 2) enlargement – which means it is getting larger A A’

15. Chapter 9.7 Common Core G.SRT.2 & G.SRT.3 – Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar… Objective – To identify similarity transformations and verify properties of similarity.

16. Chapter 9.7 Notes Two figures are similar if and only if there is a similarity transformation that maps one figure onto the other.