Which of the following conditions make a pair of triangles congruent?

a) One angle and two sides are congruent.
b) Two angles and one side are congruent.
c) Two corresponding sides and one angle are congruent.
d) Two corresponding sides and two corresponding angles are congruent.

We will use the concept of congruency of triangles to answer this question.

Answer: Options (b) and (d) are correct.

Let's see how we can use the concept of congruency of triangles.

Explanation:

Let us look at each of the options to identify the right option.

Option (a): When we talk about the congruency of triangles given a pair of congruent angles and two pairs of congruent sides, then it must fall in the SAS. But it is not necessary that given one congruent angle and two congruent sides follow the SAS rule. So, option (a) is not correct.

Option (b): Given two pairs of congruent angles and a pair of congruent sides, then it must fall in the AAS rule or ASA rule. This is certain that if we have two pairs of congruent angles and a pair of congruent sides, then it will definitely fall in either of the two rules of congruent triangles. So, option (b) is correct.

Option (c): The explanation for option c) is the same as for option a). So, option (c) is also not correct.

Option (d): Given two pairs of congruent angles and a pair of congruent sides, then it is certain that it will fall in the AAS rule or ASA rule. So, option (d) is correct.

Hence, options (b) and (d) are correct.