Answer:
AAS Postulate
Step-by-step explanation:
Understanding the question
Given the following conditions we want to find which postulate we can use to prove the triangles congruent.
To get a better visual representation of this, kindly view the attached image
As you can see, we are given that two angles are congruent as well as 1 side.
Analyzing the postulates given in the answer choices to determine the correct one that is used.
- SSS Postulate - if three sides of a triangle are congruent to the three sides of another triangle, then the triangles are congruent
- ASA Postulate - If two angles and an included side of one triangle are congruent to two angles and an included angle of another triangle, then the triangles are congruent
- SAS Postulate - If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent
- AAS Postulate - If two angles and a non included side are congruent to two angles and a non included side of another triangle, then the triangles are congruent
Because we are given two congruent angles and a congruent side, SAS and SSS are eliminated.
The difference between AAS and ASA is whether the side is included or "between" the to given angles. (see 2nd attached image)
If you view the first attached image you notice that the congruent sides are not in between the two congruent angles.
Thus, the Postulate the proves these triangles to be congruent is the AAS postulate
