The perpendicular bisector and the line along which the segment lies. If the figure has no line of symmetry indicate that fact. For each of the following figures, describe and draw all of the lines of symmetry of the figure. For example, a rectangle has two lines of symmetry, each of which is the perpendicular bisector of the sides.Ī. When the image of figure under reflection in a line is the figure itself, the line is referred to as the line of symmetry for the figure. See GSP file from Victor Brunaud-Vega for a construction and discussion. Then since the radius of the circle is known, the image circle will be a circle with center O' with the same radius. Thus in this problem, if O is the center of the circle, then the image O' will such that the segment OO' is bisected by the given line. If your construction in Case 1 uses the assumption that the image circle and the given circle will intersect, then a different construction is needed for Case 2.īy definition, a reflection in a line is a transformation of the plane such the line is the perpendicular bisector of the segment PP' where P' is the image of P. Either the line intersects the circle or it does not. Note there are two situations to consider. Describe the construction in words and state any assumptions in your construction. Construct the image of a circle under the reflection in the line. Draw a Circle and a line that does not contain a diameter of the circle. Describe your procedure and state the assumptions you are making in your solution.ģ. Construc t the image of a triangle ABC under reflection in a line l (with straightedge and compass). Perform M l, the reflection of a point in a line, byĢ.
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