$17 \cdot 195$ In parallelogram $A B C D$, $P$ is the midpoint of $B C$, a line through $P$ parallel to $B D$ intersects $C D$ at $Q$. Connect $P A$, $P D$, $Q A$, $Q B$. Then, in the figure, the number of triangles, other than $\triangle A B P$, that have the same area as $\triangle A B P$ is
(A) 3.
(B) 4.
(C) 5.
(D) 6.
(China Junior High School Mathematics League, 1985)
[Solution] From the given conditions, $Q$ is the midpoint of $CD$. In the figure, there are two types of triangles with the same area as $\triangle ABP$:
(1) Two triangles that are equal in base and height to $\triangle ABP$: $\triangle BPD, \triangle PCD$,
(2) Three triangles with one side twice the length of $BP$ and the height half of the height on $BP$: $\triangle BCQ, \triangle ADQ, \triangle QDB$.
Therefore, the answer is $(C)$.