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3.1 – Polygons and Symmetry

3.1 – Polygons and Symmetry. Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection. — Hermann Weyl , 1885-1955 (German-American Mathematician). Test Corrections.

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3.1 – Polygons and Symmetry

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  1. 3.1 – Polygons and Symmetry Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection. — Hermann Weyl, 1885-1955 (German-American Mathematician)

  2. Test Corrections Explain why the original answer was incorrect Show work/provide justification for the correct answer Staple to test Return by Friday 15 points (HW and a half) After school TODAY

  3. Do Now What do all of these letters have in common? A H I T V X Name another letter that belongs in the group What do these letters have in common? B C D E K How are the two groups related?

  4. Polygons • Review: • A polygon is a plane figure formed from three or more segments such that each segment intersects exactly two other segments, one at each endpoint, and no two segments with a common endpoint are collinear. • Key points: • Three or more segments • Each segment intersects two and only two other segments at endpoints • No two segments lie on the same line

  5. Classifying Polygons by # of Sides The prefix indicates the number of sides

  6. Other classifications • Equilateral: all segments have equal measure • Examples: • Equiangular: all angles have equal measure • Examples: • http://www.cut-the-knot.org/Curriculum/Geometry/EquiangularPoly.shtml#Explanation

  7. Regular Polygons Regular polygons are both equilateral and equiangular

  8. Reflectional Symmetry Think “Mirror Image” A figure has reflectional symmetry if and only if its reflected image across a line coincides exactly with the preimage. The line is called an axis of symmetry

  9. Alphabet Reflections Which (capital) letters of the alphabet have reflectional symmetry?

  10. Triangles • Take a look at the triangles on your notes • Scalene; Isosceles; Equilateral • Draw in any axes of symmetry you can find • Which triangles have reflectional symmetry?

  11. Rotational Symmetry An object has rotational symmetry if and only if it has at least one rotation image, not counting rotations of 0° or multiples of 360°, that coincides with the original. We describe an objects rotational symmetry by naming how many “rotational images” it has. 6-fold 2-fold 5-fold

  12. Rotational Symmetry Examples How many –fold symmetry do regular octagons have? Heptagons? n-gons? How many degrees will each rotation by in a regular polygon’s rotational symmetry? http://www.analyzemath.com/Geometry/rotation_symmetry.html

  13. Which Symmetry? Reflectional Rotational

  14. Something to think about… • What objects can you think of that have either reflectional or rotational symmetry? • Is that symmetry essential to the object’s function? • Are there any objects that need to be unsymmetrical? HOMEWORK: pg. 142 – 4, 7, 11-14, 23, 27-29, 33-39, 62

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