Chapter 8
Quadrilaterals and Polygons
A square tile can look unfamiliar when it is turned on one corner. A drawing that looks almost the same may have different side lengths or angles. When should two shapes share a name, and when should they belong to different groups? Quadrilaterals and other polygons invite us to look beyond a familiar outline. What evidence would convince someone that a shape belongs in a particular family?
What You'll Explore
6 lessons.
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What would you need to know about a shape before naming it? Compare polygons drawn in different positions, and explore how a useful system of names can describe both their differences and their connections.
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Walk around the edge of a polygon and notice each turn along the way. Investigate how a polygon's angles connect to its overall shape, then ask which regular shapes can meet without leaving gaps in a tiled floor.
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Picture a hinged frame that can tilt away from its rectangular starting shape. As you explore parallelograms, ask which relationships are worth testing and how you could move from a convincing drawing to a proof.
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Can a few markings on a quadrilateral settle what kind of shape it must be? Investigate the difference between clues that merely fit a parallelogram and evidence strong enough to prove that every possible drawing is one.
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Some parallelograms have familiar names of their own, but a familiar outline can hide the details that distinguish them. Explore rectangles, rhombi, and squares through their diagonals, and ask what evidence is enough to identify each kind.
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Which details matter when a trapezoid or kite is drawn in an unusual position? Use the definitions to investigate relationships among sides, diagonals, and symmetries, including special cases that may challenge your first impression.