Congruence vs Similarity | Difference Between Congruence and Similarity
The key differences between congruence and similarity are:
| Aspect | Congruence | Similarity |
|---|---|---|
| Definition | Geometric figures have same shape and size. | Geometric figures have same shape but not size. |
| Scale Factor | Scale factor is 1. | Scale factor can be any non-zero real number. |
| Correspondence | Corresponding sides and angles are equal. | Corresponding angles are equal, sides are proportional. |
| Transformations | Requires rigid transformations (translations, rotations, reflections). | Can involve dilation (scaling). |
| Symbol | Denoted by ≅ (congruent symbol). | Denoted by ~ (similarity symbol). |
| Ratio of Areas | Congruent figures have equal areas. | Similar figures have areas proportional to the square of the scale factor. |
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SAS Congruence Rule
SAS Congruence Rule: SAS Congruence Rule is a principle in geometry that provides a method for determining if two triangles are congruent, meaning they have the same size and shape. SAS stands for Side-Angle-Side, indicating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
Condition of Congruency of Two Triangle: When the two sides of a triangle are equal to the two sides of another triangle, and the angles formed by these sides (the included angles) are also equal, then the two triangles are congruent Congruence between any two geometric objects is represented by “≅” which reads as ‘is congruent to’.
In this article, we will discuss the SAS Congruence Rule and criteria of congruence of right-angle triangles with examples and proof.
Table of Content
- What is Congruence?
- What is SAS Congruence Rule?
- SAS Congruence Rule Definition
- Criteria for SAS Congruence Rule
- SAS Congruence Rule Proof
- How to apply SAS Congruence Rule?
- SAS Similarity Criteria
- Congruence vs Similarity | Difference Between Congruence and Similarity
- SAS Congruence Rule Class 9
- SAS Congruence Rule Solved Examples
- SAS Congruence Rule – Practice Problems