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Lesson 1.14 Activities and Cool Down

Author:
Beverly Williams, Tim Brzezinski
Topic:
Mathematics, Rotation, Geometric Transformations

Turning Into Triangles

  1. Draw a segment. Label the endpoints A and B.
    1. Rotate segment AB clockwise around center B by 90 degrees. Label the new endpoint A'.
    2. Use the Polygon tool to draw triangle ABA'.
    3. What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.

Draw a segment. Label the endpoints C and D.

  1. Rotate segment CD counterclockwise around center D by 30 degrees. Label the new endpoint C'.
  2. Rotate segment C'D counterclockwise around center D by 30 degrees. Label the new endpoint C".
  3. Use the Polygon tool to draw triangle CDC".
  4. What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.

Draw the image of quadrilateral ABCD when rotated 120 degrees 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 ABC around D so that the image of A is B?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Which segment is the image of AB when rotated 90 degrees counterclockwise around point P?

Check my answer

Here are 2 polygons:

Select all sequences of translations, rotations, and reflections below that would take polygon P to polygon Q.

Select all that apply
  • A
  • B
  • C
  • D
  • E
Check my answer (3)

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'.

  1. Explain why the line containing AB is parallel to the line containing A'B'.

Check my answer

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':

Andre tried to rotate triangle ABC 45 degrees counterclockwise. He knows something went wrong because the image doesn’t seem to be congruent to the original figure.

1.         What is one idea that Andre probably understands about rotations?

1.         What is one idea that Andre doesn’t understand about rotations?

Andre Step 1

Andre Step 1

Andre Step 2

Andre Step 2

Andre Step 3

Andre Step 3

Rotate triangle ABC by 45 degrees counterclockwise, avoiding Andre’s mistake.

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