![postulate geometry postulate geometry](https://www.onlinemath4all.com/images/aaspostulate.png)
SAS Theorem (Side-Angle-Side)īy applying the Side Angle Side Postulate (SAS), you can also be sure your two triangles are congruent. You will see that all the angles and all the sides are congruent in the two triangles, no matter which ones you pick to compare. So go ahead look at either ∠ C and ∠ T or ∠ A and ∠ T on △ C A T.Ĭompare them to the corresponding angles on △ B U G. The postulate says you can pick any two angles and their included side. You may think we rigged this, because we forced you to look at particular angles. You can only make one triangle (or its reflection) with given sides and angles. This is because interior angles of triangles add to 180 °. This forces the remaining angle on our △ C A T to be: The two triangles have two angles congruent (equal) and the included side between those angles congruent. See the included side between ∠ C and ∠ A on △ C A T? It is equal in length to the included side between ∠ B and ∠ U on △ B U G. Notice that ∠ C on △ C A T is congruent to ∠ B on △ B U G, and ∠ A on △ C A T is congruent to ∠ U on △ B U G. In the sketch below, we have △ C A T and △ B U G. An included side is the side between two angles. The Angle Side Angle Postulate (ASA) says triangles are congruent if any two angles and their included side are equal in the triangles. Let's take a look at the three postulates abbreviated ASA, SAS, and SSS. Testing to see if triangles are congruent involves three postulates.
![postulate geometry postulate geometry](https://i.ytimg.com/vi/yvANNSspYE8/maxresdefault.jpg)
More important than those two words are the concepts about congruence. Do not worry if some texts call them postulates and some mathematicians call the theorems.