2. Made By : Jai Hans
Class : 8 – F
Roll Number : 28
3. CURVES
A plane curve is a curve that lies in a single plane or a
plane surface like paper. A plane curve may be closed or
open.
4. POLYGONS
Polygon is a closed
plane figure bounded
by three or more
straight sides that meet
in pairs in the same
number of vertices, and
do not intersect other
than at these vertices.
5. PARTS OF A POLYGON
- The endpoints of the sides of polygons are called vertices. When
naming a polygon, its vertices are named in consecutive order
either clockwise or counterclockwise.
Consecutive sides are two sides that have an endpoint in
common. The four-sided polygon in Figure below could have
been named ABCD, BCDA, or ADCB, for example. It does not
matter with which letter you begin as long as the vertices are
named consecutively. Sides AB and BC are examples of
consecutive sides.
There are four pairs of
consecutive sides in
this polygon.
6. PARTS OF A POLYGON
A diagonal of a polygon is any segment that joins two
nonconsecutive vertices. Figure shows five-sided
polygon QRSTU. Segments QS , SU , UR , RT and QT are
the diagonals in this polygon.
Diagonals of a polygon can be found with the
formula given below :
7. CLASSIFICATION OF POLYGONS
Polygons first fit into two
general categories— convex and
concave.
A polygon is concave if there are
two points somewhere inside it for
which a segment with these as its
endpoints cuts at least 2 of the sides
of the polygon.
A polygon that is not concave is
called convex.
9. CLASSIFICATION OF POLYGONS
Polygons are also classified by how many sides (or
angles or vertices) they have. The following lists the
different types of polygons and the number of sides that
they have:
A triangle is a three-sided polygon
A quadrilateral is a four-sided polygon.
A pentagon is a five-sided polygon.
A hexagon is a six-sided polygon.
A septagon or heptagon is a seven-sided polygon.
An octagon is an eight-sided polygon.
A nonagon is a nine-sided polygon.
A decagon is a ten-sided polygon
10. REGULAR POLYGONS
When a polygon is both equilateral and equiangular, it
is referred to as a regular polygon. For a polygon to be
regular, it must also be convex.
.
11. SUM OF INTERIOR ANGLES OF POLYGON
Sum of the interior angles of a polygon = (N - 2) x 180°
Note: Sum of exterior angles of any polygon is always 360
degrees & the sum of interior angles of a polygon can be more
or less than 360 degrees which can be calculated by the
formula given above.
12. A Quadrilateral is any shape with 4 sides . The word
“quadrilateral” comes from two Latin words “quadri”
which means ‘a variant of four’ and “lateral” which
means side.
PROPERTIES:
with four sides
with four angles
with four vertices
With one pair of diagonals
QUADRILATERALS
13. Interior Angle Sum Property: According to this
property, the sum of the interior angles of the
quadrilateral is 360°
Exterior Angle Sum Property: According to this
property, the sum of the exterior angles of the
quadrilateral is 360°
QUADRILATERALS
15. Types of Quadrilaterals
RECTANGLE
Opposite sides are parallel and congruent .
The diagonals bisect each other.
The diagonals are congruent.
A rectangle is a four-sided shape where every angle is
a right angle (90°).
16. RHOMBUS
A rhombus is a four-sided shape where all sides have
equal length.
Also opposite sides are parallel and opposite
angles are equal.
Another interesting thing is that the diagonals
(dashed lines in second figure) of a rhombus bisect
each other at right angles.
17. SQUARE
A square has equal sides and every angle is a right angle
(90°)
A square can be thought of as a special case of other
quadrilaterals, for example:
a rectangle but with adjacent sides equal
a parallelogram but with adjacent sides equal and the
angles all 90°
a rhombus but with angles all 90°
18. PARALLELOGRA
MA parallelogram is
a quadrilateral with opposite
sides parallel. Also opposite angles
are equal (angles "a“ is same as
angles "b“ ). The opposite sides are
equal .The adjacent angles are
supplementary and the diagonals
bisects each other ; but they are
not equal.It is the "parent" of some other quadrilaterals, which are
obtained by adding restrictions of various kinds:
A rectangle is a parallelogram but with all four interior
angles fixed at 90°.
A rhombus is a parallelogram but with all sides equal in
length.
A square is a parallelogram but with all sides equal in
19. TRAPEZIUM
Trapezoid Isosceles Trapezoid
A trapezium is quadrilateral which has at least one pair
of parallel sides .
It is called an Isosceles trapezium if the sides that aren't
parallel are equal in length and both angles coming from
a parallel side are equal
Note : Trapezium is UK terminology & in US terminology it is called as
Trapezoid.
20. KITE
Two pairs of adjacent sides of a kite are equal in length.
One pair of opposite angles (the ones that are between
the sides of unequal length) are equal in size.
One diagonal bisects the other.
Diagonals intersect at right angles.
A kite is a quadrilateral whose
four sides can be grouped
into two pairs of equal-length
sides that are adjacent to
each other.
Kite quadrilaterals are named
for the wind-blown,
flying kites, which often have
this shape
