Basic Proportionality Theorem (Thales Theorem)
Basic Proportionality Theorem, also known as Thales’ Theorem, is a fundamental concept in geometry that relates to the similarity of triangles. It states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. In simpler terms, if a line parallel to one side of a triangle intersects the other two sides, it divides those sides proportionally.
Mathematically, if a line DE is drawn parallel to one side of triangle ABC, intersecting sides AB and AC at points D and E respectively, then according to the Basic Proportionality Theorem:
BD/DA = CE/EA
This theorem is a consequence of the similarity of triangles formed by the parallel line and the sides of the original triangle. Specifically, triangles ADE and ABC, as well as triangles ADC and AEB, are similar due to corresponding angles being equal. Consequently, the ratios of corresponding sides in similar triangles are equal, leading to the proportionality relationship described by the Basic Proportionality Theorem.
Basic Proportionality Theorem is widely used in geometry and trigonometry to solve various problems involving parallel lines and triangles. It serves as a foundational principle for understanding the properties of similar triangles and the relationships between their corresponding sides and angles. Additionally, it forms the basis for more advanced concepts in geometry, such as the Parallel Lines Theorem and applications in various geometric constructions and proofs.
Similar Triangles
Similar Triangles are triangles with the same shape but can have variable sizes. Similar triangles have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles are different from congruent triangles. Two congruent figures are always similar, but two similar figures need not be congruent.
Two triangles are considered similar when their corresponding angles match and their sides are proportional. This means that similar triangles have the same shape, although their sizes may differ. On the other hand, triangles are defined as congruent when they not only share the same shape but also have corresponding sides that are identical in length.
Now, let’s learn more about similar triangles and their properties with solved examples and others in detail in this article.
Table of Content
- What are Similar Triangles?
- Similar Triangles Definition
- Similar Triangles Examples
- Basic Proportionality Theorem (Thales Theorem)
- Similar Triangles Criteria
- Similar Triangles Formula
- Formula for Similar Triangles in Geometry
- Similar Triangle Rules
- Angle-Angle (AA) or AAA Similarity Theorem
- Side-Angle-Side or SAS Similarity Theorem
- Side-Side-Side or SSS Similarity Theorem
- How to Find Similar Triangles?
- Area of Similar Triangles – Theorem
- Difference Between Similar Triangles and Congruent Triangles
- Applications of Similar Triangles
- Important Notes on Similar Triangles
- Solved Questions on Similar Triangles
- Practice Questions Similar Triangles
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