Step-by-step explanation
Let's study each pair of triangles separately.
First we have the triangles in part a. Two sides of a triangle have the same length as other two sides in the other triangle. They also share an angle: the vertex shared by both triangles is an intersection between two lines which means that any pair of opposite angles in that intersection have the same measure. In summary, these triangles have two equal sides and an equal angle that is not the angle between those sides. The only triangle congruence rule that uses two pairs of equal sides and one pair of equal angles states that the triangles are congruent if the angles are the ones between the two sides considered on each triangle. This is not the case so these two triangles are not necessarily congruent.
In part b we have two triangles that have two pairs of equal angles and a pair of equal sides. According to the Angle-Side-Angle (ASA) rule these triangles are congruent.
In part c we have two triangles and we only know that there are two pairs of equal sides. There's no congruence rule that only requires two equal sides so these triangles are not necessarily congruent.
In part d we have two triangles with two pairs of equal corresponding sides and a pair of equal corresponding angles. In each triangle the angle belonging to that last pair is located between the sides of equal length. Then according to the Side-Angle-Side (SAS) rule these two triangles are congruent.
Answers
a. Not necessarily congruent.
b. Congruent due to the Angle-Side-Angle congruence rule (ASA).
c. Not necessarily congruent.
d. Congruent due to the Side-Angle-Side congruence rule (SAS).