M8 – BPW – Investigation 1 and 2

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Butterflies,

Pinwheels, and Wallpaper

Investigation #1 and 2 Symmetry, Transformations and Congruence

Name________________________________________________

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Butterflies, Pinwheels, and Wallpaper

Investigation #1 – Symmetry and Transformations Problem 1.1 – What does it mean to say that a figure has flip or reflectional symmetry? How is each point related to its image under transformation by reflection in a line? Problem 1.2 – What does it mean to say that a figure has turn or rotational symmetry? How is each point related to its image under transformation by rotation? Problem 1.3 – What does it mean to say that a figure has slide or translational symmetry? How is each point related to its image under transformation by translation? Problem 1.4 – How, if at all, will the shape, size, and position of a figure change after each of the transformations—reflection, rotation, or translation?

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1.

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Homework #1:

1. Fill in the blanks with an equivalent math term.

a. Another word for a flip is _________________________.

b. Another word for a slide is __________________________.

c. Another word for a turn is __________________________.

2. Choose the transformation preformed on each of the following.

a.

b.

3. How many lines of symmetry does the following diagram have? _________

4. Quadrilateral ABCD and its image under a counterclockwise

rotation are shown. a. Label A’, B’, C’, D’ on the image.

b. What is the center of rotation? Explain how you know.

H

a. Translation

b. Reflection

c. Dilation

d. Rotation

e.

a. Translation

b. Reflection

c. Dilation

d. Rotation

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Homework #2

1. Determine the number of lines of symmetry for each figure below.

a. ________________________ b. ________________________ c. _________________________

2. Determine all types of symmetry the shape below has. Also determine the basic

design element for each type. a. __________________________ symmetry

b. __________________________ symmetry

3. Which graph(s) at right represent a reflection?

4. Which graph(s) at right represent a

rotation?

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Are the triangles congruent?

Are the triangles congruent?

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Are the triangles congruent?

Are the triangles congruent?

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Are the triangles congruent?

Are the triangles congruent?