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- 1. Basic Geometrical Ideas
- 2. • Curves: Curves can be defined as figures that flow smoothly without a break. A line is also a curve, and is called a straight curve. • Any drawing (straight or non-straight) drawn without lifting the pencil from the paper and without the use of a ruler is called a curve. In everyday use curve means ‘not straight’ but in mathematics, a curve can be a straight line also. • Example of curves:
- 3. Types of Curve: • Simple Curve: The curve which does not cross itself. From the above, image (ii), (iii), (vi) and (vii) are simple curves as they do not cross themselves. • Open Curve: The curve which does not form a closed path. From the above, image (iii), (vi) and (vii) are the open curves. • Not Simple Curve: The curve which does not cross itself. From the above, image (i), (iv) and (v) are not simple curves as they cross themselves. • Closed Curve: The curve which form a closed path. From the above, image (i), (ii), (iv) and (v) are the closed curve. Position in a Figure: In a closed curve, there are three position. • Interior or inside of the curve. • Boundary or on the curve. • Exterior or outside the curve.
- 4. Interior of the curve. Here, point P lies inside the circle. Boundary of the curve. Here, point P is on the circle. Exterior of the curve. Here, point P lies outside the circle.
- 5. Polygons A polygon is a closed figure bounded by three or more line segments that intersect exactly to form a closed curve. Some examples of polygon,
- 6. Basic Terms in Polygons Sides: The line segments that forms a polygon is termed as sides. From the above polygon, we can say that line segment AB, BC, CD, DA are four sides of the polygon. Vertex: The meeting of two sides is termed as vertex. From the above polygon, we can say that A is a vertex as DA and AB meets at A. Similarly, B, C and D are also vertices of the polygon. Adjacent Sides: In a polygon, any two sides that has a common end are termed as adjacent sides. From the above polygon, we can say that sides CD and BC are adjacent as they terminate at a common end C. Similarly, sides AB and DA, AB and BC, CD and DA are also adjacent. Adjacent Vertices: End points of the same side of the polygon are termed as adjacent vertex. From the above polygon, we can say that C and D are adjacent vertices while A and C are not adjacent vertices. Diagonals: The line joining the non-adjacent vertices of a polygon is termed as diagonals. From the above polygon, we can say that line segment AC and DB are the diagonals of the polygon.