The Third Angles Theorem states the following.
If two angles of a triangle are congruent to
two angles of a second triangle,
then the third angles are also congruent.
Let's also recall the definition of triangle congruence.
Two triangles are congruent
if and only if
all corresponding angles and sides are congruent.
Let's put these together to prove the statement in the question.
Given:& Two pairs of corresponding congruent angles and
& Three pairs of corresponding congruent sides
Prove:& the two triangles are congruent
Proof:
