Map a Polygon Onto Itself

Describe the rotational symmetry for a regular pentagon.

• A regular pentagon has a central angle of 72° and will map onto itself after rotations of 72°, 144°, 216°, and 288°.

• A regular pentagon has five axes of symmetry.

• A regular pentagon has four-fold rotational symmetry.

• A regular pentagon has a central angle of 45° and will map onto itself after rotations of 45°, 90°, 135°, 180°, 225°, 270°, and 325°.

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CCSS.HSG.CO.A.3

Which transformation carries the parallelogram below onto itself?

• a reflection over y = x

• a reflection over y = −x

• a rotation of 90° counterclockwise about the origin

• a rotation of 180° counterclockwise about the origin

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CCSS.HSG.CO.A.3

Which of the following transformations carry this regular polygon onto itself?

• Rotation of 144 degrees counterclockwise

• Rotation of 120 degrees counterclockwise

• Rotation of 90 degrees counterclockwise

• Rotation of 64 degrees counterclockwise

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CCSS.HSG.CO.A.3

Select each answer choice that will map the regular polygon onto itself?

• 36 degree rotation

• 90 degree rotation

• 180 degree rotation

• 252 degree rotation

• 270 degree rotation

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CCSS.HSG.CO.A.4

Which of the following lines of reflection will map the polygon onto itself?

• x = 3

• x = -1

• y = -1

• y = 3

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CCSS.HSG.CO.A.3

The figure shows two perpendicular lines, and , intersecting at a point P in the interior of a trapezoid. Line is parallel to the bases and bisects both legs of the trapezoid. Line bisects both the bases of the trapezoid. Which transformation will carry the figure onto itself?

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CCSS.HSG.CO.A.3

The figure below shows two perpendicular lines 𝑗 and 𝑘 intersecting at point 𝐷 in the interior of a rectangle. Line 𝑗 bisects both the top and bottom sides of the rectangle. Line 𝑘 bisects both the left and right sides of the rectangle. Which transformation will always carry the figure onto itself? Select All that apply.

• a reflection across line 𝑗.

• A reflection across line 𝑘.

• A rotation of 90° clockwise about point 𝐷.

• A rotation of 180° clockwise about point 𝐷.

• A rotation of 270° clockwise about point 𝐷.

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CCSS.HSG.CO.A.3

Which transformation will map the right triangle onto itself?

• 90 degree rotation

• 180 degree rotation

• 270 degree rotation

• none of the above choices

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CCSS.HSG.CO.A.3

Which transformation will map the rectangle onto itself?

• 90 degree rotation about the center point

• 180 degree rotation about the center point

• reflection across the x axis

• reflection across the bue line

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CCSS.HSG.CO.A.3

Which line of reflection will NOT carry the square onto itself?

• y = 0

• x = 0

• y = x

• x = 5

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CCSS.HSG.CO.A.3