IM Geo.1.14 Lesson: Defining Rotations

For each figure, which pair of angles appears congruent? How could you check?
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[/img][/color]
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[/img]
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[/img]
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[/img]
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
[table][tr][td]If your teacher gives you the data card:[/td][td]If your teacher gives you the problem card:[/td][/tr][tr][td][list=1][*]Silently read the information on your card.[/*][*]Ask your partner “What specific information do you need?” and wait for your partner to ask for information. Only give information that is on your card. (Do not figure out anything for your partner!)[/*][*]Before telling your partner the information, ask “Why do you need to know (that piece of information)?”[/*][*]Read the problem card, and solve the problem independently.[/*][*]Share the data card, and discuss your reasoning.[/*][/list][/td][td][list=1][*]Silently read your card and think about what information you need to answer the question.[/*][*]Ask your partner for the specific information that you need.[/*][*]Explain to your partner how you are using the information to solve the problem.[/*][*]When you have enough information, share the problem card with your partner, and solve the problem independently.[/*][*]Read the data card, and discuss your reasoning.[/*][/list][/td][/tr][/table]
Do not show or read your card to your partner.
Use the applet below:
[size=150]Draw a segment. Label the endpoints [math]A[/math] and [math]B[/math].[/size][br][list][*]Rotate segment [math]AB[/math] clockwise around center [math]B[/math] by 90 degrees. Label the new endpoint [math]A'[/math].[/*][*]Use the Polygon tool to draw triangle [math]ABA'[/math].[/*][/list][br]What kind of triangle did you draw?
What other properties do you notice in the figure? Explain your reasoning.
Use the applet below:
[size=150]Draw a segment. Label the endpoints [math]C[/math] and [math]D[/math].[/size][br][br][list][*]Rotate segment [math]CD[/math] counterclockwise around center [math]D[/math] by 30 degrees. Label the new endpoint.[/*][*]Rotate segment [math]C'D[/math] counterclockwise around center [math]D[/math] by 30 degrees. Label the new endpoint [math]C''[/math].[/*][*]Use the Polygon tool to draw triangle [math]CDC''[/math].[/*][/list][br]What kind of triangle did you draw?
What other properties do you notice in the figure? Explain your reasoning.
You constructed an equilateral triangle by rotating a given segment around one of its endpoints by a specific angle measure.
An equilateral triangle is an example of a [i]regular polygon[/i]: a polygon with all sides congruent and all interior angles congruent. Try to construct some other regular polygons with this method.

IM Geo.1.14 Practice: Defining Rotations

Draw the image of quadrilateral ABCD when rotated 120° counterclockwise around the point D.
There is an equilateral triangle, ABC, inscribed in a circle with center D.
What is the smallest angle you can rotate triangle [math]ABC[/math] around  so that the image of [math]A[/math] is [math]B[/math]?
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[/img][br]Which segment is the image of [math]AB[/math] when rotated [math]90°[/math]counterclockwise around point [math]P[/math]?
The semaphore alphabet is a way to use flags to signal messages. Here's how to signal the letter Q.
[img]data:image/png;base64,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[/img][br]Describe a transformation that would take the right hand flag to the left hand flag.
Here are 2 polygons:
[img]data:image/png;base64,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[/img][br][br]Select [b]all [/b]sequences of translations, rotations, and reflections below that would take polygon [math]P[/math] to polygon [math]Q[/math].[br]
Draw the image of figure ABC when translated by directed line segment u. Label the image of A as A', the image of B as B', and the image of C as C'.
Explain why the line containing [math]AB[/math] is parallel to the line containing [math]A'B'[/math].
There is a sequence of rigid transformations that takes A to A', B to B', and C to C'. The same sequence takes D to D'. Draw and label D':

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