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Chapter 10

Chapter 10. Polygons and Area. Section 10-1. Naming Polygons. Regular polygon. A polygon that is both equilateral and equiangular. Convex Polygon. If all of the diagonals lie in the interior of the figure, then the polygon is convex. Concave Polygon.

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Chapter 10

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  1. Chapter 10 Polygons and Area

  2. Section 10-1 Naming Polygons

  3. Regular polygon • A polygon that is both equilateral and equiangular

  4. Convex Polygon • If all of the diagonals lie in the interior of the figure, then the polygon is convex.

  5. Concave Polygon • If any point of a diagonal lies outside of the figure, then the polygon is concave.

  6. Section 10-2 Diagonals and Angle Measure

  7. Theorem 10-1 • If a convex polygon has n sides, then the sum of the measures of its interior angles is (n-2)180

  8. Theorem 10-2 • In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360.

  9. Section 10-3 Areas of Polygons

  10. Postulate 10-1 • For any polygon and a given unit of measure, there is a unique number A called the measure of the area of the polygon

  11. Postulate 10-2 • Congruent polygons have equal areas

  12. Postulate 10-3 • The area of a given polygon equals the sum of the areas of the nonoverlapping polygons that form the given polygon.

  13. Section 10-4 Areas of triangles and trapezoids

  14. Theorem 10-3 • If a triangle has an area of A square units, a base of b units, and a corresponding altitude of h units, then A = ½ bh

  15. Theorem 10-4 • If a trapezoid has an area of A square units, bases of b1 and b2 units, and an altitude of h units, then A = ½ h(b1 +b2)

  16. Section 10-5 Areas of regular polygons

  17. Center • A point in the interior of a regular polygon that is equidistant from all vertices

  18. Apothem • A segment that is drawn from the center that is perpendicular to a side of the regular polygon

  19. Theorem 10-5 • If a regular polygon has an area of A square units, and apothem of a units, and a perimeter of P units, then A = ½ aP

  20. Significant digits • All digits that are not zeros and any zero that is between two significant digits • Significant digits represent the precision of a measurement

  21. Section 10-6 symmetry

  22. symmetry • If you can draw a line down the middle of a figure and each half is a mirror image of the other, it has symmetry

  23. Line symmetry • If you can draw this line, the figure is said to have line symmetry • The line itself is called the line of symmetry

  24. Rotational symmetry • If a figure can be turned or rotated less than 360° about a fixed point so that the figure looks exactly as it does in its original position, it has rotationalorturn symmetry

  25. Section 10-7 tessellations

  26. tessellations • A tiled pattern formed by repeating figures to fill a plane without gaps or overlaps

  27. Regular tessellation • When one type of regular polygon is used to form a pattern

  28. Semi-regular tessellation • If two or more regular polygons are used in the same order at every vertex

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