What are Similar Triangles?
Similar triangles are triangles that look similar to each other, but their sizes might be different. Similar objects are of the same shape but different sizes. This implies similar shapes, when magnified or demagnified, should superimpose over each other. This property of similar shapes is known as “Similarity“.
There are three similar triangle theorems:
- AA (or AAA) or Angle-Angle Similarity Theorem
- SAS or Side-Angle-Side Similarity Theorem
- SSS or Side-Side-Side Similarity Theorem
Similar Triangles Definition
Two triangles are called similar triangles if their corresponding angles are equal and the corresponding sides are in the same proportion. The corresponding angles of two similar triangles must be equal. Similar triangles can have different respective lengths of the sides of the triangle, but the ratio of lengths of corresponding sides must be the same.
When two triangles are similar it implies that:
- All pairs of corresponding angles in the triangles are equal.
- All pairs of corresponding sides of the triangle are proportional.
The symbol “∼” is used to represent the similarity between similar triangles. So, when two triangles are similar, we write it as △ABC ∼ △DEF.
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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