L9.6 New

Geometry:

Geometry Chapter 9 Lesson 6

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SOLUTION EXAMPLE 1 Identify lines of symmetry How many lines of symmetry does the hexagon have? a. b. c. a. Two lines of symmetry. b. Six lines of symmetry. c. one line of symmetry. SOLUTION SOLUTION

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GUIDED PRACTICE for Example 1 How many lines of symmetry does the object appear to have? 1. 2. 3. ANSWER 8 ANSWER 5 ANSWER 1

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GUIDED PRACTICE for Example 1 4. Draw a hexagon with no lines of symmetry. ANSWER

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EXAMPLE 2 Identify rotational symmetry Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself. a. Parallelogram SOLUTION a. The parallelogram has rotational symmetry. The center is the intersection of the diagonals. A 180° rotation about the center maps the parallelogram onto itself. o

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EXAMPLE 2 b. The regular octagon has rotational symmetry.The center is the intersection of the diagonals. Rotations of 45 , 90 , 135 , or 180° about the center all map the octagon onto itself. o o o Identify rotational symmetry b. Regular octagon SOLUTION

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EXAMPLE 2 c. The trapezoid does not have rotational symmetry because no rotation of 180° or less maps the trapezoid onto itself. Identify rotational symmetry c. Trapezoid SOLUTION

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GUIDED PRACTICE for Example 2 Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself. 5. Rhombus 6. Octagon 7. Right triangle SOLUTION yes; 180° about the center SOLUTION yes; 90° or 180° about the center SOLUTION no

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EXAMPLE 3 Standardized Test Practice

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EXAMPLE 3 Writing Reciprocals The correct answer is B. SOLUTION The triangle has line symmetry. Three lines of symmetry can be drawn for the figure. 360 s o 360 3 o o For a figure with s lines of symmetry, the smallest rotation that maps the figure onto itself has the measure . .So, the equilateral triangle has or 120 rotational symmetry.

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GUIDED PRACTICE for Example 3 8. Describe the lines of symmetry and rotational symmetry of a non-equilateral isosceles triangle. The altitude, No rotational symmetry ANSWER