Muskan Gaba[Vll E-23] Group Leader

Naman Aggarwal[Vll E-24]

Nandita Verma [Vll E-25]Navjot Singh[Vll E-26]Parishi Gupta [Vll E-27]Pranav Shrivastava[Vll

E-28]Priyanshi Goel[Vll E-29]

Group 4 Vii E

TRIANGLE & ITS

PROPERTIES

A Presentation By- Group 4

INTRODUCTION …A triangle is a 3-sided

polygon. Every triangle has three

sides, three vertices and three angles. On the basis of sides of a triangle, triangles are

of three types, Equilateral, Isosceles and Scalene Triangle

& On the basis of angles of a triangle,

they are also of three types, acute angled, obtuse angled and

right angled triangle.

Medians Of A TriangleThe line segment joining a Vertex of the triangle to the mid-point of the Opposite sides, is called the median of a triangle.

The point of concurrency of the medians of a triangle is called centroid.

A triangle can have 3 medians . The medians of a triangle can not lie outside the triangle.

Example:-Q-Draw a

triangle and name it as

ABC. Draw a median from A to the mid-point of BC.

B CD

A So, AD is the

median of the triangle ABC

Altitudes Of A Triangle Altitude of a triangle is the

line segment from the vertex of a triangle and is perpendicular to the opposite side.

The point of concurrency of the triangle is called the orthocentre.

A triangle can have 3 altitudes.

The altitudes of a triangle can lie outside the triangle.

Q-Draw a triangle and name it as

PQR. Draw an altitude from

vertex P which is

perpendicular to QR

Example:-

Q RS

PSo, AD is the altitude of the triangle ABC

angle sum propertyThe sum of the

angles of a triangle is always 180.

This property of a triangle is called

angle sum property.

In a triangle ABC, if angle a is 30

degrees & angle b is 45 degrees.

Find angle c

Example:-Q-A- Let angle c be xa + b + c= 180 (sum of all

the angles of a triangle is 180)

30+45+x=18075+x=180X=180-75

x=105Thus, c=105

Exterior Angle Of A Triangle & Its PropertyThe angle formed

outside a triangle by extending any of the 3 sides of triangle is called exterior angle of triangle.

The exterior angle of a triangle is always equal to sum of interior opposite angles.

Example:-

S

P

RQ105

45

Find Angle RPQQuestion-Let angle RPQ be x Angle PQR + Angle RPQ =Angle PRS (Exterior Angle

Property)45+x=105x=105-45

x=60Thus, Angle RPQ=60

Equilateral TriangleA triangle

having all sides of equal

length is equilateral triangle.

All sides have the same length.

Each angle have the same measure.

As the sum of three angle is 180 degree, each angle has measure 60 degrees.

Isosceles TriangleA

triangle having

two sides of equal length is isosceles triangle.

Two sides are of equal length.

The angles opposite to equal sides are also equal.

Perpendicular from vertex bisects the base.

Sum & difference of the lengths of two sides of a triangle

1. Sum of the lengths of any two sides of a triangle is greater than the length of the third side.

2. Difference between the lengths of any two sides of a triangle is smaller than the length of the third side

Pythagoras PropertyThe side opposite to

the right angle is called hypotenuse ; the other two sides are called the legs of the triangle.

In a right angled

triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

hypotenuse

legleg

Example:-A

CB

In triangle ABC, Find AC, If AB=6cm &

BC= 8cm

By Pythagoras Property,(Hypotenuse) =(Perpendicular) + (Base)

So, AC = AB +BCAC =6 + 8AC =36+64

AC =100AC = 10

Thus, AC =10 cm

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Any Questions? ?