Rectilinear figures
Rectilinear figures: A plane figure bounded by straight lines is called a rectilinear figure.
Polygon: A closed rectilinear figure having three or more sides is called a polygon.
For n (³ 3), let P1, P2,... Pn be distinct points in a plane, if the n line segments P P1 P2 P2 P3, .
(i) no two line segments intersect except at their end points.
(ii) no two line segments with a common end point are collinear.
Then the union of the n line segments P1 P2, P2P3 .. PnP1 is called a polygon with vertices P1, P2 ..., Pn and denoted by
Polygon P1 P2 ... Pn.
Each of the n line segments forming a polygon is called its side. The angle determined by two sides meeting at a vertex is called an angle of the polygon.
KINDS OF POLYGONS
Convex: If each interior angle of a polygon is less than 180°, the polygon is convex. If for each side of the polygon, the line containing that side has all the other vertices on the same side of it.
Concave: If at least one interior angle of a polygon is greater than 180°,. the polygon is concave.
Regular: If all the sides of a polygon are equal and all the angles are equal, the polygon is called a regular polygon.
Polygon Note 1: Polygon are given special names according to the number of sides they have:
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Number of sides
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Name of Polygon
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3
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Triangles
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4
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Quadrilateral
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5
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Pentagon
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6
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Hexagon
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7
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Heptagon
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8
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Octagon
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9
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Nonagon
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10
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Decagon
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11
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Dodecagon
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h
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n-gon
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(b) Regular 3-sided polygon is an equilateral triangle.
(c) Regular 4-sided polygon is a square.
Note 1: Each exterior angle of a 360° regular polygon of n sides -n-.
Note 2: Each interior angle = 180° - exterior angle.
(d) In a convex polygon of n side, the sum of interior angles is equal to (2n - 4) right angles.
(e) The sum of exterior angles of a polygon is equal to 4 right angles.
(f) Sum of interior angles of a hexagon is 120°.
Quadrilateral: If A, B, C, D are four points in a plane such that no three of, them are collinear and the line segments AB, BC, CD and DA do not intersect except at their end points, the figure formed by these four segments is called a quadrilateral.
(A) A quadrilateral is a parallelogram, if
(i) its opposite sides are equal; or
(ii) its opposite angles are equal; or
(iii) its diagonals bisect each' other; or
(iv) it has one pair of opposite sides equal and parallel.
(B) The diagonals of a rhombus bisect each other at right angles.
(C) The diagonals of rectangle are equal.
(D) The diagonals of a square are equal and bisect each other at right angles.
Properties of a quadrilateral:
(1) The sum of the angles of a quadrilateral is 360°.
(2) If the sides of a quadrilateral are produced, in order, the sum of the four exterior angles so formed is 3600.
Types of quadrilateral; trapezium:
A quadrilateral having exactly one pair of parallel sides is called a trapezium.
Parallelogram: A quadrilateral in which both pairs of opposite sides are parallel, is called a parallelogram.
BASE AND ALTITUDE OF A PARALLELOGRAM
Base: A base of a parallelogram is any side of if,
Altitude or height: For each base of a parallelogram, the corresponding altitude is the line segment from a point on the base perpendicular to the line containing the opposite side.
Rhombus: A parallelogram having all sides equal is called a rhombus.
Rectangle: A parallelogram whose each angle is a right angle, is called a rectangle.
Square: A parallelogram having all sides equal and each angle equal to a right angle is called a square.
Kite: A quadrilateral having two pairs of equal adjacent sides -but unequal opposite sides is called a kite.
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