Types of Triangles Based on Angles
On the basis of angles, there are 3 types of triangles:
- Acute Angled Triangle
- Obtuse Angled Triangle
- Right Angled Triangle
Acute Angled Triangle
In Acute angle triangles, all the angles are greater than 0° and less than 90°. So, it can be said that all 3 angles are acute in nature (angles are lesser than 90°)
Properties of Acute Angled Triangles
- All the interior angles are always less than 90° with different lengths of their sides.
- The line that goes from the base to the opposite vertex is always perpendicular.
Obtuse Angled Triangle
In an obtuse angle Triangle, one of the 3 sides will always be greater than 90°, and since the sum of all three sides is 180°, the rest of the two sides will be less than 90° (angle sum property).
Properties of Obtuse Angled Triangle
- One of the three angles is always greater than 90°.
- Sum of the remaining two angles is always less than 90° (angle sum property).
- Circumference and the orthocentre of the obtuse angle lie outside the triangle.
- Incentre and centroid lie inside the triangle.
Right Angled Triangle
When one angle of a triangle is exactly 90°, then the triangle is known as the Right Angle Triangle.
Properties of Right-angled Triangle
- A Right-angled Triangle must have one angle exactly equal to 90°, it may be scalene or isosceles but since one angle has to be 90°, hence, it can never be an equilateral triangle.
- Side opposite 90° is called Hypotenuse.
- Sides are adjacent to the 90° are base and perpendicular.
- Pythagoras Theorem: It is a special property for Right-angled triangles. It states that the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular i.e. AC2 = AB2 + BC2
Triangles in Geometry
Triangles in Geometry: A Triangle is a polygon with three sides and three corners. The corners are also known as vertices, and the sides that connect them are called edges. The interior of a triangle is a two-dimensional region. A triangle is the simplest form of a Polygon.
- Triangles can be classified based on their angles: Acute-angled, Obtuse-angled, and Right-angled.
- Triangles can be classified based on their sides: Equilateral, Isosceles, and Scalene.
Triangles are fundamental geometric shapes that play a crucial role in various fields, from mathematics and architecture to engineering and art. In this comprehensive guide, we delve into the world of triangles, uncovering their diverse properties, types, and real-world applications.
Let’s learn more about what are triangles in maths, their definition, types of triangles, formulas, examples, and practice problems in the article.
Table of Content
- Triangles Definition
- Triangle Shape
- Parts of a Triangle
- Angles in a Triangle
- Examples of Triangles in Geometry
- Properties of Triangles
- Types of Triangles
- Types of Triangles Based on Sides
- Equilateral Triangle
- Properties of Equilateral Triangle
- Equilateral Triangle Formulas
- Isosceles Triangle
- Properties of Isosceles Triangle
- Scalene Triangle
- Properties of Scalene Triangle
- Types of Triangles Based on Angles
- Acute Angled Triangle
- Obtuse Angled Triangle
- Right Angled Triangle
- Angle Sum Property of a Triangle
- Triangle – Line of Symmetry
- Triangle Formulas
- Perimeter of Triangle
- Area of a Triangle
- Area of Triangle Using Heron’s Formula
- Steps to Find Area Using Herons Formula
- Congruent Triangles
- Ways to Prove Triangle Congruence:
- Properties of Congruent Triangles:
- Applications of Congruent Triangles:
- Similar Triangles
- Properties of Similar Triangles
- Formula of Similar Triangles
- Rules of Similar Triangles
- Applications of Similar Triangles
- Triangle Class 9
- Median of Triangle
- Altitude of Triangle
- Centroid of Triangle
- Circumcentre of a Triangle
- Orthocentre of a Triangle
- Incentre of a Triangle
- Fun Facts about Triangles
- Triangles Solved Examples
- Triangles in Geometry – Practice Problems
- Practice Questions on Triangles in Geometry