Triangle Pau

Govt. Ser. Sec. Model School P.A.U, Ludhiana Teacher Trainer:Harinder kaur Student Trainer:Under Guidance of – Rachna Mrs. Kusum Lata

Students Names(9th) Indermohan Singh, Sandeep Kumar, Pooja Bhatt,

Definition of triangle Triangle (geometry), geometric figure consisting of three points, called vertices, connected by three sides. In Euclidean plane geometry, the sides are straight line segments. In spherical geometry, the sides are arcs of great circles. The term triangle is sometimes used to describe a geometric figure having

Types of triangle

A triangle is a plane figure bounded by three straight lines. A scalene triangle has three sides of unequal lengths, an isosceles triangle has two equal sides, and an equilateral triangle has three equal sides. In the isosceles triangle the angles opposite the equal sides are equal,

Theorems & Properties of Triangle  On

2nd Theorem

the Basis of Sides & Angles There are Six Types of Triangle. Let us deduce this important properties of triangle.  1. Sum of the three angles of a triangle is 180 degree. 2. If a side of a triangle is produced, the exterior angle so formed is equal

Congruence of triangles  1.

Two line segment are congruent ,if they are of equal length.  2. Two angles are congruent if they have the same measure.  3. Two triangles are congruent if all the sides and all the angles of one are equal to the corresponding sides and

Theorems of congruence

 Theorem

1. Two triangle are congruent if any two side and the included angle of one triangle are equal to any two sides and the included angles of the other triangle. This relation is referred to as (SAS) side angle side axiom.

Theorem 2 of congruence nd

 Two

triangles are congruent if any two angles and included side of one triangle are equal to the two angles and the included side of the other triangle. This is called ASA ( AngleSide-Angle) criterion for congruence of triangles.

Theorem 3 of congruence rd

 Two

triangles are congruent if the three sides of one triangle are equal to the three sides of the other triangle. It is called SSS Congruence of triangle. As shown below:-

Theorem 4 of congruence th

 Two

triangles are congruent if the three angles of one triangle are equal to the three angles of the other triangle. It is called AAA Congruence of triangle. As shown below:-

Theorem 5 of congruence th

 Two

Right triangles are congruent if the hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of other triangle. It is called RHS (Righthypotenuse-side). Given Below:-

Inequalities in a triangle

 Theorem

1:- If two sides of a triangle are unequal, the larger side has the greater angle opposite to it. For example:ab=4cm, ac=6cm,bc=5cm. The Greater angle is angle B.

Theorem 2

nd

 The

sum of any two sides of triangle is greater than the third side. For example: ab + bc > ac (2+4 >5).  bc + ca > ab(4+5 >2).  ca + ab > bc(5+2 >4).

Theorem 3

rd

 The

Difference of any two sides of triangle is lesser than the third side. For example: bc - ab < ac (4-2 <5).  ca - bc < ab(5-4 <2).  ca - ab < bc(5-2 <4).

Heron Formula  It

was discovered by Greek Mathematician Hero of Alexandria. He was born in egypt. Heron Formula is as follows: Semi perimeter = ½ (a + b + c).  By Heron Formula area of triangle =  s(s-a) (s-b) (s-c)