![]() ![]() Plane back to the same point (in the same way that □ maps 3 to 3, □ to □, and so forth). Transformation, like the function □ defined on the real number line by the equation □(□) = □, maps each point in the Transformation that trivially maps any figure in the plane back to itself called the identity transformation. ![]() IDENTITY SYMMETRY: A symmetry of a figure is a basic rigid motion that maps the figure back onto itself. The method for calculating the angle of rotation, and try it out on the rectangle, hexagon, and parallelogram above. In any regular polygon, how do you determine the angle of rotation? Use the equilateral triangle above to determine You notice about the incenter and circumcenter in the equilateral triangle? In Lesson 5 of this module, you also locatedĪnother special point of concurrency in triangles-the incenter. Hence, the center of rotation of an equilateral triangle is also theĬircumcenter of the triangle. The intersection of these two bisectors gives us the center of rotation. Method is finding the perpendicular bisector of at least two of the sides. To identify the center of rotation in the equilateral triangle, the simplest Paragraph below to locate the center precisely. Identify the center of rotation in the equilateral triangle □□□ below, and label it □. When we studied rotations two lessons ago, we located both a center of rotation and an angle of rotation. Can you identify the polygon that does not have such symmetry? ROTATIONAL SYMMETRY OF A FIGURE: A nontrivial rotational symmetry of a figure is a rotation of the plane that maps theįigure back to itself such that the rotation is greater than 0° but less than 360°. What did you do to justify that the lines youĬonstructed were, in fact, lines of symmetry? How can you be certain that you have found all lines of symmetry? Then, sketch any remaining lines of symmetry that exist. Use your compass and straightedge to draw one line of symmetry on each figure above that has at least one line of ![]() Has line symmetry if there exists a line (or lines) such that the image of the figure whenĭoes every figure have a line of symmetry? Another way of thinking about line symmetry is that a figure In particular, the line of symmetry is equidistant from allĬorresponding pairs of points. Has a corresponding point on the triangle on the other side of the line of symmetry, given by Every point of the triangle on one side of the line of symmetry This line of symmetry can be thought of as a reflection across itself that takes Top vertex to the midpoint of the base, decomposing the original triangle into two congruent A line of symmetry of the triangle can be drawn from the LINE OF SYMMETRY OF A FIGURE: This is an isosceles triangle. The figure above is a 210° rotation (or 150° clockwise rotation). Vertices on the original figure and the final image. The angle of rotation is determined by connecting the center of rotation to a pair of corresponding The center of rotation is the point at which the two lines of When you reflect a figure across a line and then reflect the image across a line that intersects theįirst line, your final image is a rotation of the original figure. When you reflect a figure across a line, the original figure and its image share a line of symmetry, which we have called ![]()
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