Properties of Triangles
Various properties of triangles are,
- Angle Sum Property: The sum of all three interior angles is always 180°. Therefore. In the Triangle ΔABC shown above, ∠A+ ∠B+ ∠C= 180°, the interior angles of a triangle will be greater than 0° and less than 180°.
- A Triangle has 3 sides, 3 vertices, and 3 angles.
- Exterior angle property: The Exterior angle of a triangle is equal to the sum of Interior opposite and non-adjacent angles (also referred to as remote interior angles). In the above shown ΔABC, ∠ACD= ∠ABC+ ∠BAC
- The sum of the length of any two sides of a triangle is always greater than the third side. For example, AB+ BC> AC or BC+ AC> AB.
- The side opposite the largest angle is the largest side of the triangle. For instance, in a right-angled triangle, the side opposite 90° is the longest side.
- The perimeter of a figure is defined by the overall length the figure is covering. Hence, the perimeter of a triangle is equal to the sum of lengths on all three sides of the triangle. Perimeter of ΔABC= (AB + BC + AC)
- The difference between the length of any two sides is always lesser than the third side. For example, AB-BC< AC or BC-AC< AB
- For similar triangles, the angles of the two triangles have to be congruent to each other and the respective sides should be proportional.
- Area of Triangle: 1/2× base × height.
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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