Understanding quadrilaterals for mathematical ecucation
1.
2. A plane figure bounded by four line
segments AB,BC,CD and DA is called
a quadrilateral.
A B
D C
3. In geometry, a quadrilateral is a polygon with four
sides and four vertices. Sometimes, the term
quadrangle is used, for etymological symmetry with
triangle, and sometimes tetragon for consistence with
pentagon.
There are over 9,000,000 quadrilaterals.
Quadrilaterals are either simple (not self-intersecting)
or complex (self-intersecting). Simple quadrilaterals
are either convex or concave.
6. 6
These figures are not polygons These figures are polygons
Definition:A closed figure formed by line segments so that each
segment intersects exactly two others, but only at their
endpoints.
7. 7
Convex: No line containing a side of the polygon contains a point
in its interior
Concave:
A polygon for which there is a line
containing a side of the polygon and
a point in the interior of the polygon.
8. 8
Regular: A convex polygon in which all interior angles have the
same measure and all sides are the same length
Irregular:Two sides (or two interior angles) are not congruent.
22. *Rhombus
I have all of the properties of the
parallelogram PLUS
- 4 congruent sides
- diagonals bisect angles
- diagonals perpendicular
23. *Square
Hey, look at me!
I have all of the properties of the
parallelogram AND the rectangle AND
the rhombus.
I have it all!
24. Is a square a rectangle?
• Some people define categories exclusively, so
that a rectangle is a quadrilateral with four right
angles that is not a square.
• This is appropriate for everyday use of the words,
as people typically use the less specific word only
when the more specific word will not do.
• Generally a rectangle which isn't a square is an
oblong.
25. • But in mathematics, it is important to define
categories inclusively, so that a square is a
rectangle.
• Inclusive categories make statements of
theorems shorter, by eliminating the need for
tedious listing of cases.
• For example, the visual proof that vector
addition is commutative is known as the
"parallelogram diagram".
• If categories were exclusive it would have to
be known as the "parallelogram (or rectangle
or rhombus or square) diagram"!
26. Trapezium
I have only one set of parallel sides.
[The median of a trapezium is parallel to the
bases and equal to one-half the sum of the
bases.]
Trapezoid Regular Trapezoid
27. • It has two pairs of sides.
Each pair is made up of adjacent sides (the
sides meet) that are equal in length.
• The angles are equal where the pairs meet.
• Diagonals (dashed lines) meet at a right
angle, and one of the diagonal bisects
(cuts equally in half) the other.
Kite
28. Cyclic quadrilateral: the four
vertices lie on a circumscribed
circle.
Tangential quadrilateral: the four
edges are tangential to an inscribed
circle. Another term for a tangential
polygon is inscriptible.
Bicentric quadrilateral: both cyclic
and tangential.
Some other types of
quadrilaterals
29. The sum of all four angles of a quadrilateral is 360
.
.
A
B C
D
1
2
3
4
6
5
Given: ABCD is a quadrilateral
To Prove: Angle (A+B+C+D) =360
.
Construction: Join diagonal BD
Arun: Good morning to one and all .Today we are extremely happy to present a PowerPoint presentation on Understanding quadrilaterals. Now Jaswant of VIII-A and myself Arunprasad from VIII-A are going to present the ppt. Now Jaswant will explain about definition of a quadrilateral.