chapter 10
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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CHAPTER 10
Polygons and Area
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NAMING POLYGONS
Section 10-1
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REGULAR POLYGONA polygon that is both equilateral and equiangular
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CONVEX POLYGON If all of the diagonals lie in the interior of the figure, then the polygon is convex.
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CONCAVE POLYGON If any point of a diagonal lies outside of the figure, then the polygon is concave.
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DIAGONALS AND ANGLE
MEASURE
Section 10-2
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THEOREM 10-1 If a convex polygon has n sides, then the sum of the measures of its interior angles is
(n-2)180
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THEOREM 10-2 In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360.
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AREAS OF POLYGONS
Section 10-3
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POSTULATE 10-1For any polygon and a given unit of measure, there is a unique number A called the measure of the area of the polygon
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POSTULATE 10-2Congruent polygons have equal areas
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POSTULATE 10-3The area of a given polygon equals the sum of the areas of the nonoverlapping polygons that form the given polygon.
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AREAS OF TRIANGLES
AND TRAPEZOIDS
Section 10-4
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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
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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)
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AREAS OF REGULAR
POLYGONS
Section 10-5
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CENTERA point in the interior of a regular polygon that is equidistant from all vertices
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APOTHEMA segment that is drawn from the center that is perpendicular to a side of the regular polygon
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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
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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
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SYMMETRYSection 10-6
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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
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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
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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 rotational or turn symmetry
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TESSELLATIONSSection 10-7
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TESSELLATIONSA tiled pattern formed by repeating figures to fill a plane without gaps or overlaps
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REGULAR TESSELLATIONWhen one type of regular polygon is used to form a pattern
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SEMI-REGULAR TESSELLATION
If two or more regular polygons are used in the same order at every vertex