Symmetry

ID: domun-nabij
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Symmetry

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Problem 1

For each figure, identify any lines of symmetry the figure has.

1)

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2)

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3)

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Problem 2

In quadrilateral BADCBADC, AB=ADAB = AD and BC=DCBC = DC. The line ACAC is a line of symmetry for this quadrilateral.

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4) Based on the line of symmetry, explain why the diagonals ACAC and BDBD are perpendicular.

5) Based on the line of symmetry, explain why angles ABCABC and ADCADC have the same measure.

Problem 3

6) Three line segments form the letter Z. Rotate the letter Z counterclockwise around the midpoint of segment BCBC by 180 degrees. Describe the result.

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Problem 4

7) There is a square, ABCSABCS, inscribed in a circle with center DD. What is the smallest angle we can rotate around DD so that the image of AA is BB?

a) 45  45^{\circ} \text{ }b) 60  60^{\circ} \text{ }c) 90  90^{\circ} \text{ }d) 180 180^{\circ}
Problem 5

8) Points AA, BB, CC, and DD are vertices of a square. Point EE is inside the square. Explain how to tell whether point EE is closer to AA, BB, CC, or DD.

Problem 6

9) Lines ll and mm are perpendicular.

Sometimes reflecting a point over mm has the same effect as rotating the point 180 degrees using center PP. Select all labeled points which have the same image for both transformations. Write each corresponding letter in the answer box and separate letters with commas.

a) A \quad\quad b) B \quad\quad c) C \quad\quad d) D \quad\quad e) E

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Problem 7

Here is triangle POGPOG followed by images of four rotations of POGPOG. Match each description below with one of the images. Write the number of the corresponding image in the answer box.

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10) Rotate 60 degrees clockwise around O.

11) Rotate 120 degrees clockwise around O.

12) Rotate 60 degrees counterclockwise around O.

13) Rotate 60 degrees clockwise around P.