Equilateral Triangle
In an Equilateral triangle, all three sides are equal to each other as well as all three interior angles of the equilateral triangle are equal.
Since all the interior angles are equal and the sum of all the interior angles of a triangle is 180° (one of the Properties of the Triangle). We can calculate the individual angles of an equilateral triangle.
∠A+ ∠B+ ∠C = 180°
∠A = ∠B = ∠C
Therefore, 3∠A = 180°
∠A= 180/3 = 60°
Hence, ∠A = ∠B = ∠C = 60°
Properties of Equilateral Triangle
- All sides are equal.
- All angles are equal and are equal to 60°
- There exist three lines of symmetry in an equilateral triangle
- The angular bisector, altitude, median, and perpendicular line are all same and here it is AE.
- The orthocentre and centroid are the same.
Equilateral Triangle Formulas
The basic formulas for equilateral triangles are:
- Area of Equilateral Triangle = √3/4 × a2
- Perimeter of Equilateral Triangle = 3a
where, a is Side of Triangle
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