Geometry is a branch of mathematics that deals with shapes, sizes, and relative positions of figures and the properties of space. The study of congruent triangles is a major topic in geometry. The Side-Angle-Side (SAS) postulate is a fundamental theorem that can be used to determine whether two triangles are congruent. In this article, we will discuss what SAS is, how it is used to determine congruence, and provide examples of SAS congruence.

## What is SAS?

SAS is a postulate in geometry that states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In other words, if two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, then the two triangles are congruent.

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## Congruent Triangles

Congruent triangles are two triangles that have the same size and shape. This means that all corresponding sides and angles of the two triangles are equal. Congruent triangles can be rotated, reflected or translated and still remain congruent.

## SAS Postulate

The SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. This means that if the length of two sides and the angle between them in one triangle are equal to the length of two sides and the angle between them in another triangle, then the two triangles are congruent.

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## SAS Congruence Criteria

The criteria for SAS congruence are as follows:

- The two triangles must have two sides with the same length.
- The two triangles must have an angle between the two sides with the same measure.
- The included angle must be the same for both triangles.

## Examples of SAS Congruence

Here are some examples of triangles that can be proven congruent using the SAS postulate:

- Two right triangles with the same hypotenuse and one acute angle
- Two isosceles triangles with the same base angles and the same base length
- Two equilateral triangles with the same side lengths
- Two scalene triangles with two sides and the included angle being equal

The SAS postulate is a fundamental theorem that can be used to determine whether two triangles are congruent. This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. The criteria for SAS congruence are two sides with the same length, an angle between the two sides with the same measure, and the included angle must be the same for both triangles. Examples of triangles that can be proven congruent using the SAS postulate include right triangles, isosceles triangles, equilateral triangles, and scalene triangles.

The SAS postulate is a powerful tool for determining congruence between two triangles. By understanding the criteria for SAS congruence and being familiar with examples of triangles that can be proven congruent using the SAS postulate, one can determine whether two triangles are congruent.