Transformation and Symmetry

Sequences of Transformations (Rigid Motions)

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Properties of Sequences of Rigid Motions

• Size and shape stay the same.

• Angle measures stay the same.

• Area and perimeter stay the same.

• Parallel segments or lines stay parallel.

• Pre-image and image are congruent.

Sequences...

Sequences of transformations are performed by doing each transformation in the order listed. Perform the first transformation on the pre-image and each transformation after that on the image created by the previous transformation.

Example

    

The blue trapezoid is translated 4 units right and then reflected over the x-axis to form the red trapezoid.

Example

    

Square ABCD is rotated 90° counterclockwise and then reflected over the y-axis to form square A'B'C'D'.

Example

    

Triangle ABC is rotated 180° about the origin, translated 5 units down, and then reflected over the x-axis to form ∆A'B'C'.

Multiple Choice

What sequence of transformations maps the red parallelogram to the green parallelogram?

• A translation followed by a reflection.

• A rotation followed by a translation.

• A reflection followed by a translation.

• A reflection followed by a rotation.

Multiple Choice

Which sequence could be used to transform hexagon C to hexagon D?

• Translation 4 left and 2 down

• a reflection over the x-axis and a translation 6 units right

• a reflection over the y-axis and a translation 2 units down

• a counter-clockwise rotation of 90 degrees about the origin

Multiple Choice

What sequence of transformations will get you from the blue triangle BCD to the red triangle B"C"D"?

• Rotation, then Rotation

• Rotation, then Dilation

• Reflection, then Rotation

• Translation, then Reflection

Multiple Choice

What sequence of transformations could map triangle ABC to triangle A"B"C"?

• A dilation followed by a rotation.

• A translation followed by a reflection.

• A rotation about the origin followed by a translation.

• A reflection followed by a rotation.

Multiple Choice

Which of the following describes the sequence of transformations shown?

• Reflection followed by a rotation.

• Rotation followed by a translation.

• Reflection across the x-axis followed by a reflection across the y-axis.

• Translation followed by a rotation.

Line and Rotational Symmetry

Symmetry

• When an object is exactly the same as another object even if it is moved, rotated or flipped.

• Lots of real-world examples.

• "Fold" the object in half and have it perfectly overlap. (oddly-satisfying!)

Poll

Symmetric?

• Yes

• No

Poll

Symmetric?

• Yes

• No

Poll

Symmetric?

• Yes

• No

Lines of Symmetry

Cutting an object in half with a line so that it creates symmetric parts. (Folded perfectly)

Multiple Choice

How many lines of symmetry does this shape have?

• 1

• 2

• 3

• 4

Multiple Choice

Determine the number of lines of symmetry for the figure.

• 0

• 1

• 3

• 6

Multiple Choice

How many lines of symmetry does the butterfly have?

• 1

• 2

• 3

• 4

Rotational Symmetry

• When you rotate an object and it looks exactly the same.

• Order of rotation: the number of times a object looks the same as it is being rotated 360 degrees (in a circle).

• Magnitude of rotation: the angle of rotation in which the object looks the same as it goes around in a circle.

Multiple Choice

What is the order of rotation in the recycling symbol?

• 1

• 2

• 3

• 1,000

Multiple Choice

Determine the angle of rotational symmetry (magnitude) for the figure.

• None

• 60°

• 120°

• 180°

Multiple Choice

What is the order and angle of rotation (magnitude) of the flag?

• Order 2, 180 degrees

• Order 4, 90 degrees

• Order 3, 120 degrees

• Order 1, 360 degrees

Multiple Choice

Determine whether the figure has line symmetry, rotational symmetry, both, or neither.

• Rotational

• Line

• Both

• Neither

Open Ended

What could be a potential test question on this topic?

Open Ended

Is there line symmetry, rotational symmetry, or both?