Example 1 As shown in Figure 1, in $\square A B C D$, $P$ is the midpoint of side $B C$. A line parallel to $B D$ is drawn through $P$ and intersects $C D$ at point $Q$. Connect $P A$, $P D$, $Q A$, and $Q B$. In Figure 1, apart from $\triangle A B P$, there are ( ) triangles with the same area as $\triangle A B P$.
(A) 3
(B) 4
(C) 5
(D) 6
(1985, National Junior High School Mathematics League)
Explanation: As shown in Figure 1, from the given conditions, we know that $Q$ is the midpoint of $C D$. Therefore, in Figure 1, the triangles that have the same area as $\triangle A B P$ are:
(1) Two triangles that are equal in base and height to $\triangle A B P$ $(\triangle B P D, \triangle P C D)$;
(2) Two triangles that have one side twice the length of $B P$ and the height half of the height on $B P$ $(\triangle B C Q, \triangle A D Q)$;
(3) One triangle that is equal in base and height to $\triangle B C Q$ $(\triangle Q D B)$.
There are a total of 5 triangles. Therefore, the correct choice is (C).