This document discusses triangles and their properties. It defines a triangle as a closed figure with three intersecting lines and three vertices. Triangles are classified based on sides (equilateral, isosceles, scalene) and angles (right, acute, obtuse). Key properties are that interior angles sum to 180 degrees and exterior angles equal the sum of opposite interior angles. Pascal's triangle and triangle terms like medians, centroids, altitudes, and orthocentres are also explained. Finally, the document outlines uses of triangles in mathematics, engineering, and architecture.

2. TOPIC :
DIMPLE ROSE THOMAS
B.ED , MATHEMATICS
MANGALAM COLLEGE OF EDUCATION

3. CONTENTS
INTRODUCTION
 TYPES OF TRIANGLES BASED ON SIDES AND
ANGLES
 PROPERTIES OF TRIANGLE
 PASCAL’S TRIANGLE
 SOME TERMS OF TRIANGLES
 USES OF TRIANGLES IN OUR DAILY LIFE
 CONCLUSION

4. INTRODUCTION
 A closed figure formed by three
intersecting lines is called a triangle.
 A triangle has three sides, three
angles and three vertices.
Here, in triangle ABC; AB, BC and
CA are the three sides, <A, <B and
<C are the three angles and A, B
and C are the vertices.
A
B C

5. TYPES OF TRIANGLE ON THE BASIS OF SIDES
EQUILATERAL
TRIANGLE
ISOSCELES TRIANGLE
SCALENE TRIANGLE

6. TYPES OF TRIANGLES ON THE BASIS OF
ANGLES
RIGHT TRIANGLE
ACUTE TRIANGLE
OBTUSE TRIANGLE

7. PROPERTIES OF TRIANGLE
 All triangles have three sides, three angles
and three vertices.
 The sum of all angles of a triangle is 180
degrees.
 The sum of two angles of a triangle is equal to
the third angle.
 The exterior angle of a triangle is equal to the
sum of its opposite interior angles.
 triangles are 2D figures.

8. PASCALS TRIANGLE
 Pascal’s triangle is a triangular array of the
binomial coefficients. It is named after French
mathematician Blasé Pascal.
 Each number is the numbers directly above it
added together.
 PROPERTIES
 The first diagonal is just “1”.
 The second diagonal has the counting numbers.
 The third diagonal has the triangular numbers
and so on.

9. 1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
: ones :counting numbers
: triangular numbers :tetrahedral numbers

10. SOME TERMS OF TRIANGLE
 MEDIAN
 In a triangle the line joining the
vertex to the mid point of the
opposite side.
 Here; AP,BQ and CR are median.
 CENTROID
 The point of intersection of all the
three medians of a triangle.
 Here; AP,BQ and CR intersect at G.
So G is centroid of triangle ABC.

11.  ALTITUDES
 In a triangle, the perpendicular
drawn from a vertex to the opposite
side is called altitude.
 Here; AP,BQ and CR are altitudes of
triangle ABC.
 ORTHOCENTRE
 The point of intersection of all the
three altitudes of a triangle is called
orthocentre.
 Here; AP,BQ and CR intersect at H,
so H is orthocentre.

12. USES OF TRIANGLE IN OUR DAILY LIFE
 TRIANGLES IN MATHEMATICS
 Triangles feature very frequently in
the discipline of mathematics. For
example, almost all two dimensional
shapes (apart from a circle) can be
made up of a series of triangles
arranged in a certain way.
 TRIANGLES IN ENGINEERING AND
ARCHITECTURE
 Many bridges and other similar
structures are often designed to
include triangle shapes, as these
shapes are able to withstand a great
amount of pressure.

13. CONCLUSION
 Triangles are the geometric figures consisting
of three vertices, three angles and three sides.
 Triangles are classified on the basis of sides
and angles.
 Pascal’s triangular is an array of binomial
coefficients.
 Triangle has many uses in our daily life.
 There are many rules, theorems and
inequalities associated with triangles.