( Geometrical Constructions) Created By: Rameshbhai Kachadia (Math’s Teacher) K.J.Shah High School Theba

Postulate 1 (Postulate of the straight ruler) A B

Ray AB Line AB A B A B

{ Definition of a Triangle) (If points A,B and C are three non -collinear points then union of AB,BC,CA is called triangle ABC) A B C

(Definition Of a Plane Quadrilateral) (If points A,B,C,D are coplanar points, no three of them are collinear points and if AB, BC, CD, DA meet at their end points only, the union of line segments AB, BC, CD and DA is called quadrilateral ABCD) B D C X A

(Postulate of the Compass) Not only a circle can be constructed but if line segment AB and a point P are given in a plane then circle with center P and radius AB can be constructed in the plane. A B P

(Definition of perpendicular bisector of a line segment) (A line which is perpendicular to the given line segment and passes through the midpoint of the given line segment is called the perpendicular bisector of that line segment) A B

(To construct a perpendicular line to the given line through a point on it) XY

Concept of a regular polygon:- Let p 1,p 2,p 3,……p n-1.,p n be three or more than three distinct points in a plane. Let the n line-segments p 1 p 2,p 2 p 3,……p n-1 p n, p n p 1 have the properties:- 1)If any two of them intersect they do not intersect at points except at their end point. 2)The points of two line-segments with common endpoints are not co-linear, then the union of this n line- segments is called a polygon. 3)If all the sides of a polygon are congruent then the polygon is called regular polygon.

Construction of a regular Hexagon Construction of a regular Hexagon & Octagon

 (0,4 cm) O.

Construction of a regular Hexagon Inscribed in circle

Construction of a regular Hexagon Inscribed in circle O. A BC D EF

Hexagon circumscribed about a circle

O l m n o p q A B C D E F (Hexagon circumscribed about a circle)

O l m n o p q A B C D E F Hexagon circumscribed about a circle

Construction of a regular Hexagon Construction of a regular Octagon Inscribed in circle

O. Octagon inscribed in a circle A B C D E F G H

Construction of a regular Hexagon (Construction of a regular Octagon Circumscribed about a circle)

Octagon circumscribed about a circle A BC D E F G H O.

A BC D E F G H O.

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