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Angles, Polygons and Circles

Angles, Polygons and Circles

An unknown quantity can be represented by a variable

Lesson Demo

Simple open curves made up of only two lines are called angles.  Simple closed curves made up of more than two lines are called polygons.  A circle is a simple closed curve formed by a point moving at the same distance from a fixed point.
Angles, polygons and circles:

Curves:

Figures that can be drawn without lifting the pencil from the paper and without the use of a ruler are called curves.  Curves that do not cross themselves are called 'simple curves'.    In the diagram here, (i), (ii), (iv) and (v) are simple curves, while (iii) is not a simple curve.  Also, (i), (iii), (iv) are examples of closed curves, while (ii) and (v) are examples of open curves.

 An 'angle' is made up of two rays having a common end point.  The two rays forming the angle are called 'sides' of the angle, and the common end point is called the 'vertex' of the angle.  Simple closed curves made up of only line segments are called polygons.  A polygon made up of three line segments is called a triangle. For example, The triangle in the diagram is called .  Here, points A, B and C are the vertices.   are the sides, and   are the angles of the triangle.
 A four-sided polygon is said to be a quadrilateral.  Points A, B, C and D are the vertices.    are the sides, and  are the angles of quadrilateral ABCD. A quadrilateral has, in all, four pairs of adjacent sides. They are AB and BC, BC and CD, CD and DA, and DA and AB. Also, it has two pairs of opposite sides. They are AB and DC, and BC and AD.  Angles A and B, angles B and C, angles C and D, and angles D and A are said to be adjacent angles.  Angles A and C, and angles B and D are said to be pairs of opposite angles. A circle is formed by a point moving at the same distance from a fixed point.  A circle is also a simple closed curve; however, it does not have any sides or angles. The line that forms the boundary of a circle is called its circumference. The part enclosed by the circumference of a circle is called the interior of the circle.   The part left outside the circle is said to be the exterior of the circle.  Some points may lie on the circumference of the circle.

An arc is a part of the circumference of a circle.  A chord is a line segment joining two points that lie on a circle.  The part of a circle that is enclosed by a chord and an arc is called a segment of the circle.  A chord passing through the centre of the circle is called its diameter.  A diameter is the longest chord of a circle.  A diameter of a circle divides it into two halves. Each half is called a semi-circle.    A line segment that joins the centre of the circle and a point on the circumference is called the radius of the circle.  The radius of a circle is half of the diameter.  The part of a circle enclosed by two radii and an arc is called a sector