“If two angles and a side of one triangle are equal to two angles and a side of another triangle then the two triangles must be congruent.
Question:
“If two angles and a side of one triangle are equal to two angles and a side of another triangle then the two triangles must be congruent.” Is the statement true? Why?
Solution:
Yes, the statement is true because the two triangles can be congruent by either AAS or ASA congruence criteria.
Disclaimer: If corresponding angles of two triangles are equal, then the by angle sum property, the third corresponding angle will be equal. So, if we have two corresponding angles and a corresponding side are equal, then the triangles can be proved congruent by SAS congruence criteria. Therefore, ASA and SAS criteria are treated as same.