Answer: Yes , we can use both ASA Postulate or the AAS Theorem to prove the triangles congruent.
Step-by-step explanation:
- ASA postulate says that if two angles and the included side of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
- AAS Theorem says that if two angles and any one side of a triangle are congruent to two angles and any one side of another triangle, then the triangles are congruent.
In the given picture we have two triangles with one same vertex.
Thus, the angle made on same vertex are vertical angles [if two lines intersect then the opposite angles are vertical angles]
Also, vertical angles are always congruent.
Thus, we got two angles of one triangle is equal to the two angles of the next triangle, then both triangles similar by AA similarity.
And similar triangles have corresponding angles equal thus the remaining third angle must be congruent, therefore both the triangles are congruent by ASA postulate.
Also both the triangles are congruent by AAS theorem because if a triangle is congruent by ASA postulate then it is also congruent by AAS theorem.
