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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.