Suppose $D \subset M$ is a strongly minimal set definable in $M$ with parameters from $C$. We say $D$ is locally modular if for all $X, Y \subset D$, with $X = \operatorname{acl}(X \cup C) \cap D, Y = \operatorname{acl}(Y \cup C) \cap D$ and $X \cap Y \neq \varnothing$, $\dim(X \cup Y) + \dim(X \cap Y) = \dim(X) + \dim(Y)$. We prove the following theorems. Theorem 1. Suppose $M$ is stable and $D \subset M$ is strongly minimal. If $D$ is not locally modular then in $M^{eq}$ there is a definable pseudoplane. (For a discussion of $M^{eq}$ see [M, $\S A$].) This is the main part of Theorem 1 of [Z2] and the trichotomy theorem of [Z3]. Theorem 2. Suppose $M$ is stable and $D, D' \subset M$ are strongly minimal and nonorthogonal. Then $D$ is locally modular if and only if $D'$ is locally modular.