Triangles in Geometry
What is a Triangle in Maths?
A triangle is a polygon, with three sides and three vertices. A triangle also has three angles and the sum of all three angles of the triangle is 180 degrees.
What are the Triangle Formulas?
The main triangle formulas are,
Area of triangle
A = [(½) b × h
Perimeter of a triangle
P = (a + b + c)
How many Types of Triangles are there in Maths?
The six basic types of triangles are,
- Acute angle triangles
- Obtuse angle triangles
- Right angle triangles
- Scalene Triangles
- Isosceles triangles
- Equilateral triangles
What are the Properties of Triangles?
Some of the important properties of triangles are:
- Sum of all three angles of the triangle is equal to 180 degrees.
- Equal angles have equal sides opposite them.
- Sum of the length of any two sides of a triangle is always greater than the third side.
What is the difference between Scalene, Isosceles, and Equilateral Triangles?
On the basis of sides triangles are of three types:
- Scalene Triangle: A triangle with all three sides unequal is called a Scalene triangle.
- Isosceles Triangle: A triangle in which any two sides are equal is an Isosceles triangle.
- Equilateral Triangle: A triangle with all three sides equal is called an Equilateral triangle.
What is the difference between an Acute Triangle, an Obtuse Triangle, and a Right Triangle?
On the basis of angles triangles are of three types:
- Acute Triangle: A triangle with all three angles as acute angles is called an acute angle triangle.
- Obtuse Triangle: A triangle with any one angle as an obtuse angle is called an obtuse angle triangle.
- Right Triangle: A triangle with any one angle as a right angle is called a right angle triangle.
What is the Triangle where Two Sides are Equal?
A triangle where two sides are equal is called an Isosceles triangle.
What is an Equilateral Triangle?
An equilateral triangle is a type of triangle that has three equal sides and three equal angles. In an equilateral triangle:
- Side Lengths: All three sides are of the same length.
- Angle Measures: All three angles are of the same measure, and each angle in an equilateral triangle measures 60 degrees.
What is an Isosceles Triangle?
An isosceles triangle is a type of triangle that has two sides of equal length and two angles of equal measure. In an isosceles triangle:
- Side Lengths: At least two sides are of the same length, making them congruent.
- Angle Measures: The angles opposite the equal sides are also congruent, meaning they have the same measure.
How many Triangles are in a Star?
A star has 10 triangles that are,
∆ABH, ∆BIC, ∆CJD, ∆DFE, ∆EGA, ∆DGI, ∆GJB, ∆FAI, ∆JGB and ∆EHJ
How many Triangles can a Pentagon be divided into?
A pentagon is divided into six different triangles which are made using the vertices of the Pentagon.
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