IM Geo.1.15 Practice: Symmetry

For each figure, identify any lines of symmetry the figure has.
In quadrilateral BADC, AB=AD and BC=DC. The line AC is a line of symmetry for this quadrilateral.
Based on the line of symmetry, explain why the diagonals [math]AC[/math] and [math]BD[/math] are perpendicular.
Based on the line of symmetry, explain why angles [math]ABC[/math] and [math]ADC[/math] have the same measure.
Three line segments form the letter Z.
Rotate the letter counterclockwise around the midpoint of segment [math]BC[/math] by 180 degrees. Describe the result.
There is a square, ABCS, inscribed in a circle with center D.
What is the smallest angle we can rotate around [math]D[/math] so that the image of [math]A[/math] is [math]B[/math]?
Points A, B, C, and D are vertices of a square. Point E is inside the square.
Explain how to tell whether point [math]E[/math] is closer to [math]A[/math], [math]B[/math], [math]C[/math], or [math]D[/math].
Lines l and m are perpendicular.
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[/img][br]Sometimes reflecting a point over m has the same effect as rotating the point 180 degrees using center [math]P[/math]. Select [b]all[/b] labeled points which have the same image for both transformations.
Here is triangle POG and some images of the triangle POG under a specific rotation.
Match the description of the rotation with the image of POG under that rotation.
Rotate 60 degrees clockwise around [math]O[/math].
Rotate 120 degrees clockwise around [math]O[/math].
Rotate 60 degrees counterclockwise around [math]O[/math].
Rotate 60 degrees clockwise around [math]P[/math].
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Information: IM Geo.1.15 Practice: Symmetry