Proving Congruence of Triangles with SAS: Side-Angle-Side Method Explained

SAS

SAS refers to one of the methods used to prove the congruence of triangles

SAS refers to one of the methods used to prove the congruence of triangles. It stands for “Side-Angle-Side” and implies that if two triangles have two sides and the included angle in common, then the triangles are congruent.

Here’s an example to illustrate SAS:

Suppose we have two triangles, triangle ABC and triangle DEF, and we want to prove that they are congruent using SAS.

First, we need to establish that two sides of triangle ABC are equal to two corresponding sides of triangle DEF. Let’s say that side AB is equal to side DE, and side BC is equal to side EF.

Secondly, we need to prove that the included angle between these two sides in triangle ABC is equal to the included angle in triangle DEF. Let’s say that angle BAC is equal to angle EDF.

Now, if we have successfully shown that side AB is equal to side DE, side BC is equal to side EF, and angle BAC is equal to angle EDF, we can conclude that triangle ABC is congruent to triangle DEF by the SAS congruence criteria.

It’s important to note that proving SAS may not always be possible, as having just two sides and an included angle in common does not always guarantee congruence. Other congruence criteria, such as Side-Side-Side (SSS), Angle-Angle-Side (AAS), or Hypotenuse-Leg (HL), may need to be used in different cases.

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