This lesson is designed for older students who have a solid understanding of shapes and focuses on many of the vocabulary words used in geometrical transformations. The aim of this material is to expose students to the vocabulary and concepts they will encounter while studying geometrical transformations so that the material becomes familiar. The focus of this lesson is not mastery of a particular topic.[br][br]This lesson can function either as an instructional support resource for you as an instructor OR equally as well as a lesson which students can directly interact with; use it in whatever way best suites your classroom needs.

This lesson focuses on developing the following standards from the state of Utah's expectations for 8th grade geometry. These standards are [i]not[/i] fully met by this lesson, but significant progress is made towards their fulfillment.[br][br][b]Standard 8.G.1[/b][br]Verify experimentally the properties of rotations, reflections, and translations:[list=1][*]Lines are taken to lines, and line segments to line segments of the same length.[br][/*][*]Angles are taken to angles of the same measure.[br][/*][*]Parallel lines are taken to parallel lines.[/*][/list][br][b]Standard 8.G.2[/b][br]Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

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[b]Angle[/b]: A way to measure how much one line turns away from another line.[br][br][b]Axis[/b]: A fixed line in space around which an object can rotate.[br][br][b]Congruent[/b]: When two shapes are exactly the same in size and shape, though they may be turned or flipped differently.[br][br][b]Dilation[/b]: Making a shape bigger or smaller while keeping its angles the same.[br][br][b]Distance[/b]: The measurement of how far apart two points are.[br][br][b]Orientation[/b]: A description of which direction an object is facing. It tells you how the object is turned, while location tells you where it is.[br][br][b]Plane[/b]: A two dimensional grid that extends forever in two independent directions (most often represented as left/right and up/down on a piece of paper). A plane can have any orientation in three dimensional space.[b][br][br]Polygon[/b]: Any closed, two dimensional figure with three or more sides.[br][br][b]Reflection[/b]: A transformation that flips a shape over a line to create a mirror image.[br][br][b]Rotation[/b]: A transformation where a shape is turned around a fixed point or axis.[br][br][b]Scale Factor[/b]: A number that describes how much bigger or smaller a dilated shape will be. For example, if this number were 2, the dilated shape would be twice as large as the original.[br][br][b]Similar:[/b] When two shapes are the same shape, but they might be turned or flipped differently. They don't have to be the same size.[br][br][b]Symmetry[/b]: When a shape can be divided into parts that are exactly the same, either by flipping (reflectional symmetry) or turning (rotational symmetry).[br][br][b]Transformation[/b]: A process that changes a shape’s size, position, or direction. Examples include moving, flipping, rotating, and resizing a shape.[br][br][b]Translation[/b]: Moving a shape from one place to another without rotating or flipping it.

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In this lesson, we will begin learning about some of the concepts that regularly appear in geometry, particularly in the use of transformations to manipulate closed shapes on a 2D plane. Watch the video below to get an idea of the concepts we will be learning about in this lesson.[br][br][b]Note:[/b] The video refers to "enlargements," but this is just another word for dilation. Enlargement is not always a great choice of vocabulary, because sometimes we are actually shrinking the shape, not making it larger. For this reason, dilation is in general a better term for this transformation.

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The exploration activities below are designed to help you see some of the properties that occur when we use the 4 transformations mentioned in the video above. Make sure to record your answers in your workbook (included below)![br][br]For each of the 4 exploration activities below, choose [b][u]one[/u][/b] of the following to complete.[br][br][b]A)[/b] Write down your own answers to two of the questions asked in the activity.[br][br][b]B)[/b] Work through the activity with a partner. Discuss what you learned from the activity. Then, write down your partner's name and key points of your discussion for the activity.[br][br][b]C)[/b] Write a multiple choice question related to the activity. Clearly mark the correct answer and explain why this answer is the correct answer to the question you wrote.[br][br][b]D) [/b]Draw a visual aide that you could use to teach someone else about this concept.[br][br][b]E)[/b] Find an example of this property out in the real world. Include an image, video, URL, or other resource that clearly demonstrates the principle, and then briefly explain how it does.[br][br][b]Note[/b]: You [b]are not required[/b] to complete the same option for each activity. Simply mark on your worksheet which option you chose for each activity.[br][br]

Translate the large triangle so that all the angles of the same color match up exactly. Click and drag to translate.[br][br]What do you notice about each of these angles? Does the size of the triangle have any impact on the size of the angles inside? What kinds of things are the same in each triangle? What is different?

Use the activity below to rotate the dashed figure. [br][br]Along the way, what do you notice? How many times does the dot land on a place that matches up with the shape in the background? If the blue dot were [i]not[/i] on the dashed figure, would you be able to tell whether or not the dashed figure had been rotated?

Use the buttons and slider to change the sizes of the polygons on the plane.[br][br]How would you describe the changes you see? Do you notice any patterns about how the shapes change in size? What happens when the scale factor is negative?

Use translations, rotations, reflections, and dilations to place the green shape (or one of its images) directly onto the solid black shape.[br][br]The [color=#38761d]GREEN[/color] shape can be translated across the plane.[br][br]The [color=#b45f06]ORANGE[/color] dot can be used to rotate the green shape.[br][br]The [color=#cc0000]RED[/color] dot will change the line of reflection.[br][br]The [color=#1155cc]BLUE[/color] dot represents the center of dilation.[br][br]What about these shapes is similar? What about them is different? Could we describe these shapes as being the same shape? Why or why not?

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Now that you have more practice understanding spatial orientation, use what you have learned to try and beat this game!