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Transformations - Renert

James McKee, Renert School, Sep 15, 2019

Explore congruence transformations in Geogebra.

Symmetry
1. Lines of Symmetry
2. Symmetry - TED video
3. Lines of Symmetry
4. Symmetrical Artist
5. Symmetry
6. Playing with symmetry
7. Assymmetry - TED video
Create lines of symmetry
1. Clover
2. Red Vase
3. Elephant
4. Black and White Flower
5. Flag
6. Building
7. Bridge
Rotational Symmetry - advance
1. Rotational Symmetry
2. Order of rotational symmetry of regular polygons
3. Rotational and Reflection Symmetry
4. Folding: Investigating Lines of Symmetry
5. Rotational Symmetry 旋轉對稱
6. Rotational Symmetry
7. Copy of Order of rotational symmetry
8. Copy of Rotational Symmetry
9. Copy of Rotational Symmetry
Transformations
1. Three types of transformations
2. Translations and Rotations
3. How to Translate a Point
4. How to Rotate a Point
5. How to reflect a point
6. Les F /1
7. Les F/5
8. Les F /2
9. Les F /3
10. Les F /4
Transformations Snakes
1. Serpentine /7B
2. Serpentine /7A
3. Serpentine /6
4. Serpentine /5B
5. Serpentine /5A
6. Serpentine /4B
7. Serpentine /4A
8. Serpentine /3B
9. Serpentine /3A
10. Serpentine /2
11. Serpentine /1
Rotations
1. Rotations: Introduction
Dilatations
1. Dilating a Point (Intro)
2. Dilating a Line: HSG.SRT.A.1.A
3. Dilating a Segment: HSG.SRT.A.1.B
4. Properties of Dilations
5. AA Similarity Theorem
Fun!
1. Messing With Lisa
2. Manipulating a Reflected Image
3. Flip Flop
4. Transformations Game
5. Flor
6. Stejnolehlost
7. Two Color Star
8. Girl in the Mirror
Exercises
1. Transformations: Exercise 1

Information

Symmetry

Lines of Symmetry

Create lines of symmetry

Clover

Rotational Symmetry - advance

1. Rotational Symmetry
2. Order of rotational symmetry of regular polygons
3. Rotational and Reflection Symmetry
4. Folding: Investigating Lines of Symmetry
5. Rotational Symmetry 旋轉對稱
6. Rotational Symmetry
7. Copy of Order of rotational symmetry
8. Copy of Rotational Symmetry
9. Copy of Rotational Symmetry

Rotational Symmetry

Transformations

Three types of transformations

Transformations Snakes

Serpentine /7B

Rotations

1. Rotations: Introduction

Rotations: Introduction

The applet below was designed to help you better understand what it means to rotate a point about another point. In the applet below, feel free to change the locations of point A and point B. Interact with this applet for a few minutes, then answer the questions that follow.

Questions: 1) Regardless of the amount of rotation, how does the distance AC compare to the distance AB? 2) Notice how, in the applet above, the angle of rotation could be positive or negative. From what you've observed, what does it mean for a rotation angle to have positive orientation? What does it mean for an angle of rotation to have negative orientation? Explain.

7.

Dilatations

1. Dilating a Point (Intro)
2. Dilating a Line: HSG.SRT.A.1.A
3. Dilating a Segment: HSG.SRT.A.1.B
4. Properties of Dilations
5. AA Similarity Theorem

7.1.

Dilating a Point (Intro)

The following applet illustrates what it means to dilate a point about another point. You can move point O (the center of dilation) and point A anywhere in the plane. You can also change the scale factor (k) of this dilation by either moving the slider or by typing it in the white box at the top of the applet. A' = the image of point A under dilation about point O with scale factor k. Interact with the applet below for a few minutes BEFORE clicking the "Check This Out!" checkbox in the lower right corner. After interacting with this applet for a bit, please answer the questions that follow the applet. (You'll be prompted to click the "Check This Out!" checkbox in the directions below.)

Questions: (Please don't click the "Check This Out!" box yet!) 1) What vocab term would you use to describe the locations of point A and A' with respect to O? In essence, fill in the blank: "The image of a point (A) under a dilation about another point (O) is a point (A') that is _____________________ with O and A. 2) Click the "Check This Out!" box now. Move point(s) O and A around. Be sure to adjust the scale factor (k) of this dilation as well. Describe what you observe. 3) Answer the additional questions on the sheet provided to you in class.

7.2.

7.3.

7.4.

7.5.

8.

Fun!

8.1.

Messing With Lisa

Note: LARGE POINTS are MOVEABLE.

8.2.

8.3.

8.4.

8.5.

8.6.

8.7.

8.8.

9.

Exercises

1. Transformations: Exercise 1

9.1.

Transformations: Exercise 1

In the applet below, a pink rectangle and an unfilled rectangle are shown. Your job is to use the transformational tools of GeoGebra to superimpose (map) the pink rectangle perfectly onto the blank rectangle. To see your work presented in a different context (problem) at any time, select the New Context button. To remove the pink shading from the original rectangle, slide the given slider to the left. Feel free to move any of the white points around (at any time) to change the size of the original rectangle. To create a new exercise, select the refresh icon in the upper right hand corner.

Questions: 1) What transformation(s) did you use in your mapping? 2) What is common about all these transformations you've listed?

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