Similar Triangles
Definition: Similar triangles are triangles that have the same shape but not necessarily the same size. In other words, their corresponding angles are equal, and their corresponding sides are in proportion.
Properties of Similar Triangles
- Corresponding Angles: Corresponding angles of similar triangles are congruent.
- Proportional Sides: Corresponding sides of similar triangles are in proportion. This means that if two triangles are similar, the ratio of the lengths of their corresponding sides is constant.
- Equal Ratios: The ratios of corresponding sides are equal. For example, if two sides of one triangle are in a ratio of 2:3 to the corresponding sides of another triangle, then all sides of the triangles are in this ratio.
Formula of Similar Triangles
The formula to determine if two triangles are similar is known as the “Angle-Angle (AA) Similarity Criterion” or “AA Postulate.” It states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Another important formula related to similar triangles is the “Side-Side-Side (SSS) Similarity Criterion.” It states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.
Rules of Similar Triangles
- AA Similarity: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
- SSS Similarity: If the corresponding sides of two triangles are in proportion, then the triangles are similar.
- SAS Similarity: If two sides of one triangle are in proportion to two sides of another triangle, and the included angles are congruent, then the triangles are similar.
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