A Project on Triangle and its Properties Submitted

A Project on Triangle and its Properties Submitted to DIRECTOR GENERAL SCHOOL EDUCATION(PB. )

Submitted By • Class IX Students of Govt. High School, Dhobra, V. P. O Jhakolari, Dt- Gurdaspur, Punjab. Under the guidance of Maths Master’s Sh. Tilak Raj, Sh. Jugal Kishore and Computer Faculty Sh. Neeraj Sharma. emailus: ghs. dhobra. gsp@gmail. com

Triangles

If A, B, C are three non Collinear points , the figure made up by three line segments AB, BC and CA is called a triangle A B C

The Six elements of a triangle are 1. Side AB 2. Side BC 3. Side AC 4. Angle ABC 5. Angle ACB 6. Angle BAC A B C

Various types of triangles • Equilateral triangle 5 cm

Isosceles triangle 5 cm 3 cm

Scalene triangle 10 cm 5 cm 6 cm

Acute triangle 40 60 80

Right triangle 90

Obtuse Triangle 120

Perimeter of a Triangle 5 cm 4 cm Perimeter=5 cm+4 cm=14 cm

Properties of Triangles

Angle sum property of a Triangle • The sum of the angles of a triangle is 180˚. A A C B

Angle sum property of a Triangle 4 5 3 1 Angle 4 + Angle 3 + Angle 5=180º Angle 1 + Angle 3 + Angle 2=180º 2

Exterior & Interior Opposite Angles B A C D

Exterior angle property of a Triangle B A C Angle A + Angle B = Angle BCD D

Exterior angle property of a Triangle B A C Angle A + Angle BCA=180º D Angle BCA + Angle BCD=180º Angle A + Angle B +Angle BCA= Angle BCA+ Angle BCD

Triangle Inequality Property • The sum of any two sides of a triangle is greater than the third side. A AB+BC >AC B C AB+AC>BC AC+BC>AB

Triangle Inequality Property A B AB+BC >AC C

Triangle Inequality Property A B AB+AC>BC C

Triangle Inequality Property A B AC+BC>AB C

Pythagoras Theorem • In a right triangle, the square of the longest side is equal to the sum of squares of remaining two sides. A Perpendicular Hypotenuse B C Base ( AC) 2 = (AB) Hypotenuse 2 2 + (BC) 2 = Perpendicular 2 + Base 2

Queries • • • What is Triangle? What are collinear points? What are the types of triangle? What is Pythagoras Theorem? What is the angle sum property of triangle?

Bibliography & References • Bibliography contains references to all the articles & pictures related to the project. It includes the documentation & Project Plan. • Standards • • Mathematics Books of Class 6 th – 10 th Internet Articles from Encarta Encyclopedia Newspapers, Charts , Models& Magazines

Acknowledgement • We express our gratitude to school Headmistress Miss Jatinder Kaur, Math’s Masters Sh. Tilak Raj & Sh. Jugal Kishore and especially Computer Faculty Sh. Neeraj Sharma for providing guideline and help. • This project has not been possible without the help of my teachers and friends and their support and encouragement. We worked hard in obtaining the facts and finding related to project which made my project more interesting.

Thanks • Thanks for being patient.