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This lesson covers the concepts of reflections and symmetry in geometric shapes. A line of symmetry divides a shape into two congruent parts, ensuring that corresponding points on either side are equal in distance from the line. The lesson includes identifying lines of symmetry in tessellations, exploring shapes related by reflection, and completing shapes based on their lines of symmetry. Through examples and solutions, students learn to recognize and analyze symmetry in various geometric forms.
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Date: ______________ Math 9/9H 7.5 Reflections and Symmetry A line of symmetry divides a shape into two congruent parts (recall that “congruent” means “equal”) • Each point on one side of the line of symmetry has a corresponding point on the other side of the line, and each of these points is the same distance from the line of symmetry • A line of symmetry is also called a line of reflection; if a mirror is placed along one side of a shape, the reflection image and the original shape together form one larger shape • The line of reflection is a line of symmetry of this larger shape
Date: ______________ Math 9/9H Example 1: Identifying Lines of Similarity in Tessellations Tessellation: a pattern made up of one or more shapes, completely covering a surface without any gaps or overlaps Identify the symmetry in each tessellation:
Date: ______________ Math 9/9H Solution: • Has one line of symmetry – each point on one side of the line has a corresponding point on the other side. The pattern on one side of the line of symmetry is a mirror image of the pattern on the other • Has 4 lines of symmetry – for each line, a point on one side of the line has a corresponding point on the other side.
Date: ______________ Math 9/9H Example 2: Identifying Shapes Related by a Line of Reflection Identify the triangles that are related to the shaded triangle by a line of reflection, and describe the position of each line of symmetry
Date: ______________ Math 9/9H Solution: Triangle A is the reflection image of the shaded triangle in the vertical line through 5 on the x-axis Triangle B is the reflection image of the shaded triangle in the horizontal line through 3 on the y-axis Triangle C is not a reflection image of the shaded triangle Triangle D is the reflection image of the shaded triangle in the oblique line that passes through (1, 9) and (9, 1)
Date: ______________ Math 9/9H Example 3: Completing a Shape Given its Line of Symmetry Quadrilateral ABCD is part of a larger shape. • Draw the image of ABCD after each reflection described. • Write the coordinates of the larger shape formed by ABCD. • Describe the larger shape and its symmetry
Date: ______________ Math 9/9H A) Reflection in the horizontal line through 2 on the y-axis. • The larger shape ABCC’B’ has coordinates A(2,2), B(4,4), C(6,4), C’(6,0), B’(4,0). This shape is a pentagon with a horizontal line of symmetry that passes through 2 on the y-axis.
Date: ______________ Math 9/9H B) Reflection in the vertical line through 6 on the x-axis. • The larger shape ABB’A’ has coordinates A(2,2), B(4,4), B’(8,4), A’(10,2). This shape is a trapezoid with a vertical line of symmetry that passes through 6 on the x-axis.
Date: ______________ Math 9/9H C) Reflection in an oblique line passing through (0,0) and (6,6). • The larger shape AD’C’BCD has coordinates A(2,2), D’(2,6), C’(4,6), B(4,4), C(6,4), D(6,2). This shape is a concave hexagon with an oblique line of symmetry that passes through (0,0) and (6,6). Please complete p.358 # 4, 5, 7abc, 8, 9, 10 • Please complete p.358 # 4, 5, 7abc, 8
