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What is Geometry? What are some key concepts? How is geometry used? What are some adjectives that describe geometry? (ex fun, creative, boring, …) Where does geometry show up in the classroom? How does geometry connect with other areas of math or other subjects?

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What is Straight? “Straight is that of which the middle is in front of both extremities” Plato “A straight line is a line that lies symmetrically with the points on itself” Euclid

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When do you call a line straight? Try to build a notion of straightness based on your experiences rather than accept a certain number of assumptions Though it is difficult to formalize, straightness is a natural human concept How do you check in a practical way that something is straight? Ex: hanging a painting on the wall

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Symmetries of a Line Reflection symmetry Half-turn symmetry

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Isometries and Symmetries An isometry is a transformation that preserves distances A symmetry of a figure is an isometry of a region of space that takes the figure onto itself What other symmetries does a line have?

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Straightness on a Sphere Paths that are instrinsically straight on a sphere (or other surface) are called geodesics At every point and in every direction on a smooth surface there is a unique geodesic going from that point in that direction All geodesics on spheres are great circles

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Why do we care? When do we use “straight” lines? What do we do with straight lines?

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