understanding quadrilaterals

1. Presented by Srashti Nagori
Class 8 th
Section B
Roll No 26

2. Geometry starts with a point which is dimensions. A point
has no length, no breadth and no height.
C
Two straight lines either intersect or are B
parallel
If two lines intersect, they have only one point
of intersection; o
for example, AB and CD intersect at a point.
D
A

3. A four sided plane figure is called a quadrilateral
If we join four non-collinear points A,B,C,D, taken
two at a time, we get six different lines through them
namely AB, BC, CD, DA, AC and BD. The first four A
enclose a quadrilateral ABCD and the remaining two B
make its two diagonals.
A quadrilateral has four vertices, four sides and two D C
diagonals.

4. Convex quadrilateral and
Concave quadrilateral
Convex quadrilateral Concave quadrilateral
In convex quadrilateral, both the diagonals If a quadrilateral contains any one side
lie in the interior of the quadrilateral. such that when it is produced, the
quadrilateral does not wholly lie on one of
In a convex quadrilateral, line segment its sides, i.e., a part of it lies on the
joining any two points lying in its interior opposite side of the produced side, then
region completely lies in the quadrilateral. the quadrilateral is said to be concave.
In convex quadrilateral, both diagonals In a concave quadrilateral, two of the
intersect inside the quadrilateral. sides are such that when they are
produced, they divide the interior of the
If in a quadrilateral, any one side is quadrilateral in two parts.
produced and the quadrilateral completely
lies one side of it, then the quadrilateral is In concave quadrilaterals, one diagonal
convex. lies in the interior and the other lies in the
exterior of the quadrilateral.

5. Closed figure
When three lines intersect at three different points, they
enclose a closed figure called triangle.
A closed figure formed by four straight lines intersecting at four
different points is called a quadrilateral.
 Properties of angles of a quadrilateral
(i) In a convex quadrilateral, all the four angles are less than
180 degree.
(ii) In a concave quadrilateral, one of the angles lies between
180 degree and 360 degree.
(iii) Sum of all the angles of a quadrilateral is 360 degree.

6. A four sided plane figure with no set pattern is simply called a quadrilateral. Some
special quadrilateral are:
Parallelogram
A quadrilateral with two pairs of opposite sides parallel is called a parallelogram.

7. Rhombus
A parallelogram with all sides equal is called rhombus.
Rectangle
A parallelogram with one angle measuring 90 degree is called a
rectangle. (The other three angles will also be 90 degree each).

8. Square
A rhombus with one angle measuring 90 degree is called a square. (The other
three angles will also be 90 degree each).
Trapezium
A quadrilateral with only pair of opposite sides parallel, is called a trapezium.

9. Kite
A quadrilateral with two pairs of adjacent sides equal is called a kite.
Angles of a quadrilateral
Four sides of a quadrilateral form four angles at their four
vertices. Four angles of the quadrilateral ABCD are <ABC,
<BAD, <BCD, <CDA. They can also be written as <A, <B,
<C, <D

10. Submitted to
Meeta ma’am
Maths teacher
Thank You!