Proving Triangle Congruence with SAS Criterion: Side-Angle-Side Explanation and Example

SAS

In mathematics, SAS stands for Side-Angle-Side

In mathematics, SAS stands for Side-Angle-Side. It is a criterion used to prove that two triangles are congruent.

If two triangles have two pairs of corresponding sides that are congruent, and the included angles between those sides are also congruent, then the two triangles are congruent based on the SAS criterion.

Let’s take an example to understand this criterion better. Consider two triangles, triangle ABC and triangle DEF.

We are given:
Side AB is congruent to side DE.
Side BC is congruent to side EF.
Angle BAC is congruent to angle EDF.

To prove that triangle ABC is congruent to triangle DEF using the SAS criterion, we need to show that all corresponding sides and angles are congruent.

Based on the given information, we can conclude that side AC is congruent to side DF, as it is the common side between the two triangles.

We have already established that side AB is congruent to side DE, and side BC is congruent to side EF.

Now, let’s examine the angles. We are given that angle BAC is congruent to angle EDF.

Using the SAS criterion, we have proven that triangle ABC is congruent to triangle DEF.

In conclusion, the SAS criterion is a useful tool to determine congruence between two triangles when we know that two pairs of corresponding sides are congruent, along with the included angle between those sides being congruent.

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