Geometry
Polygon
Any figure bounded by three or more line segments is called a polygon. A regular polygon is one in which all sides are equal and all angles are equal. A regular polygon can be inscribed in a circle. The name of polygons with three, four, five, six, seven, eight, nine and ten sides are respectively triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon and decagon.
Convex Polygon
In a convex polygon, a line segment between two points on the boundary never goes outside the polygon. More precisely, in a convex polygon no internal angle can be more than\[180{}^\circ \].
Convex polygon
Concave Polygon
In a concave polygon, a line segment between two points on the boundary goes outside the polygon.
or
In a concave polygon atleast one of the interior angle is more than\[180{}^\circ \].
Concave polygon
Some important Formulae
(i) Sum all the angles in a convex polygon is\[(2n-4)90{}^\circ \].
(ii)Exterior angle of a regular polygon is\[\frac{360{}^\circ }{n}\].
(iii)Interior angle of a regular polygon is\[\left( 180{}^\circ -\frac{360{}^\circ }{n} \right),\] where n is number of sides of the polygon
(iv) Number of diagonals of a convex polygon of n sides is\[\frac{n\left( n-3 \right)}{2}\].
Quadrilaterals
A plane closed figured bounded by four segments is called quadrilateral.
The sum of four angles of a quadrilateral is equal to\[360{}^\circ \].
If the four vertices of a quadrilateral lie on the circumference of a circle i.e. if the quadrilateral can be inscribed in a circle it is called a cyclic quadrilateral. In a cyclic quadrilateral, the sum of opposite angles \[=180{}^\circ \], i.e. \[A+C=180{}^\circ \]and \[B+D=180{}^\circ \]
Parallelogram
A quadrilateral having opposite sides are parallel is called a parallelogram. In a parallelogram,
(i) opposite sides are equal.
(ii) opposite angles are equal.
(iii) each diagonal divides the parallelogram into two congruent triangles.
(iv) sum of any two adjacent angles is\[180{}^\circ \].
(v) the diagonals bisect each other.
Rhombus
A parallelogram is a rhombus is which every pair of adjacent sides are equal (all four sides of a rhombus are equal).
Since, a parallelogram is a rhombus, all the properties of a parallelogram apply to a rhombus. Further, in a rhombus, the diagonals are perpendicular to each other.
Rectangle
A parallelogram is a rectangle in which each of the angles is equal to\[90{}^\circ \]. The diagonals of a rectangle are equal.
A rectangle is also a special type of parallelogram and hence all properties of parallelogram apply to rectangles also.
Square
A rectangle is a square in which all four sides are equal (a rhombus in which all
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