A triangle is a 3-sided polygon with three sides, three vertices, and three angles. Triangles can be categorized based on their side lengths as either equilateral (all sides equal), isosceles (two sides equal), or scalene (no sides equal). They can also be categorized based on their angle measures as either acute (all angles less than 90 degrees), obtuse (one angle greater than 90 degrees), or right (one angle of 90 degrees). The study of triangles, known as triangle geometry, contains many beautiful theorems and relationships.

1. TRIANGLES

3. TRIANGLES
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, An Equilateral
Triangle, An Isosceles Triangle and A Scalene Triangle. All
triangles are convex and bicentric. That portion of the plane
enclosed by the triangle is called the triangle interior, while
the remainder is the exterior.
The study of triangles is sometimes known as triangle
geometry and is a rich area of geometry filled with
beautiful results and unexpected connections.

4. On Basis of Length of Sides, there are 3 types of Triangles
• Equilateral Triangle
• Isosceles Triangle
• Scalene Triangle
On Basis of Angles, there are 3 types of triangles
• Acute Angled Triangle
• Obtuse Angled Triangle
• Right Angled Triangle

5. EQUILATERAL TRIANGLE
Triangles having all sides equal are called Equilateral
Triangle.
ISOSCELES TRIANGLE
Triangles having 2 sides equal are called Isosceles
Triangle.

6. SCALENE TRIANGLE
Triangles having no sides equal are called Scalene
Triangle.

7. Triangles whose all angles are acute angle are called
Acute Angled Triangle.
ACUTE ANGLED TRIANGLE
RIGHT ANGLED TRIANGLE
OBTUSE ANGLED TRIANGLE
Triangles whose 1 angle is obtuse angle are called
Obtuse Angled Triangle.
Triangles whose 1 angle is right angle are called
Right Angled Triangle.

8. MEDIAN OF A TRIANGLE

12. CONGRUENCY OF A TRIANGLE

15. HERON’S FORMULA
Heron’s Formula can be used in finding area of
all types of Triangles. The Formula is :-
S = Semi-Perimeter
a,b,c are sides of the Triangle

16. Pythagoras Theorem