Presentation on theme: " The surface which is flat and plane is known as plane surface. For example paper. A curve in the plane whose starting point is also the end point."— Presentation transcript:
The surface which is flat and plane is known as plane surface. For example paper. A curve in the plane whose starting point is also the end point and which has no other self- intersections. A simple closed curve is also known as Jordan curve
SSimple closed curve made up of line segments is called polygon. CURVES THAT ARE POLYGONS Example 1 CURVES THAT ARE NOT POLYGONS Example 2
Number of sides or vertices ClassificationSample of figure 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon
A diagonal is a line segment connecting two non – consecutive vertices of a polygon.
The polygon, in which all the diagonals lie in interior is known as convex polygon. The polygon, in which some diagonals lie in exterior is known as concave polygon.
TThe angle sum property of quadrilateral is 360. C B D A The angle sum property of triangle is 180. We have divided a quadrilateral into two triangles.So, =360
Based on the nature of the sides or angles of a quadrilateral, it gets special names.
PROPERTIES 1. A quadrilateral with each pair of opposite side parallel. 2. Opposite sides are equal 3. Opposite angles are equal. 4. Diagonals bisect each other. 5. Adjacent angles are supplementary.
PROPERTIES 1. All the sides are equal. 2. All the angles are equal. 3. The diagonals bisect each other. 4. Also a rectangle.
PROPERTIES 1. The opposite sides are equal. 2. Diagonals are equal. 3. Each of the angle is right angle. 4. A parallelogram with a right angle.
PROPERTIES 1. A parallelogram with sides of equal length. 2. All the properties of parallelogram. 3. Diagonals are perpendicular to each other.
PROPERTIES A 1. A quadrilateral with exactly two pairs of equal consec- B D utive sides. 2. The diagonals are perpendic- ular to each other. C 3. One of the diagonal bisect the other. 4. In the figure m B=m D but m A= m C
PROPERTIES 1. Trapezium is a quadrilateral with a pair of parallel sides ( NOTE: The arrow marks indicate parallel lines)