A) The first diagram is a single triangle.

Here are the answers to the questions about the matchstick pattern:

a) The first diagram is a single triangle.
You used $\boxed{\text{3 matches}}$ to make the first diagram.

b)
To make the second diagram (two triangles), you add 2 matches to the first diagram.
Total matches for the second diagram: $3 + 2 = \boxed{\text{5 matches}}$.

To make the third diagram (three triangles), you add 2 matches to the second diagram.
Total matches for the third diagram: $5 + 2 = \boxed{\text{7 matches}}$.

c) The pattern is formed by adding one triangle at a time, with each new triangle sharing one side with the previous one.

d) You had to add $\boxed{\text{2 matches}}$ each time to extend the pattern by one triangle.