Friday 26 July 2013

$Polygons$

· A polygon is a closed plane figure made up of line segments.

· The number of angles is equal to the number of sides.

Interior Angles of a Polygon

If n represents the number of sides of a polygon, then

The sum of the interior angles of the polygon

Each interior

of an n-sided regular polygon

Exterior Angles of a Polygon

Sum of the exterior angles of any polygon is

An exterior

of an n-sided regular polygon

$Geometrical Constructions and Properties$

Perpendicular Bisector of a Line Segment In the diagram, AB is the perpendicular bisector of PQ at M. · M is the midpoint of PQ. · · · Any point on AB is equidistant from P and Q.
Construction: Step 1: Taking P and Q as centres and a radius greater than half of PQ, draw arcs above and below PQ such that the arcs cut each other at A and B. Step 2: Join A to B with a straight line, bisecting PQ at M.
Angle bisector In the diagram, QC is the angle bisector of . · · · Any point on QC or QC produced is equidistant from PQ and RQ.
Construction: Step 1: With the compass point at the vertex Q and suitable radius, draw an arc cutting QP at A and QR at B. Step 2: Taking A and B as centres, and the same radius, draw arcs to cut each other at C. Step 3: Join Q to C with a straight line.