In California practice, a merger reorganization will typically involve two agreements - one short, the other not.  The Corporations Code refers to the shorter agreement as the "agreement of merger".   At a minimum it must include all of the following:

1. The terms and conditions of the merger.
2. The amendments, subject to Sections 900 and 907, to the articles of the surviving corporation to be effected by the merger, if any. If any amendment changes the name of the surviving corporation the new name may be the same as or similar to the name of a disappearing domestic or foreign corporation, subject to subdivision (b) of Section 201.
3. The name and place of incorporation of each constituent corporation and which of the constituent corporations is the surviving corporation.
4. The manner of converting the shares of each of the constituent corporations into shares or other securities of the surviving corporation and, if any shares of any of the constituent corporations are not to be converted solely into shares or other securities of the surviving corporation, the cash, rights, securities, or other property which the holders of those shares are to receive in exchange for the shares, which cash, rights, securities, or other property may be in addition to or in lieu of shares or other securities of the surviving corporation, or that the shares are canceled without consideration.
5. Other details or provisions as are desired, if any, including, without limitation, a provision for the payment of cash in lieu of fractional shares or for any other arrangement with respect thereto consistent with the provisions of Section 407.

Cal. Corp. Code § 1101(a).  The longer agreement is not required by the code and thus has no official name.  To avoid confusion, practitioners will often refer to it as the "plan of reorganization".  In addition to the foregoing, the plan of reorganization commonly includes representations and warranties, indemnities, hold back and other "deal points".   The agreement of merger must be filed with the California Secretary of State's office, the plan of reorganization is not filed with that office.  Cal. Corp. Code § 1103.

The California General Corporation Law defines a "constituent corporation" as a corporation which is merged with or into one or more other corporations or one or more other business entities and includes a surviving corporation.  A triangular merger involves a third party - a parent corporation of one of the constituent corporations.  While the parent corporation will typically be a party to the plan of reorganization, it is not required to be a party to the merger agreement.   This is stated explicitly in Section 1101(a) which provides "The constituent corporations shall be parties to the agreement of merger and other persons, including a parent party (Section 1200), may be parties to the agreement of merger". 

Section 1103 requires that an officers' certificate of each constituent corporation be filed with the agreement of merger.  If If equity securities of a parent of a constituent corporation are to be issued in the merger, the officers’ certificate of that constituent corporation must state either that no vote of the shareholders of the parent was required or that the required vote was obtained.  Id.  Note that the statute does not require that an officers' certificate of the parent corporation be filed.  Rather, the required statement must be included in the subsidiary constituent's officer certificate.

In practice, many agreements of merger include the parent corporation as a party and thus also include an officers' certificate of the parent corporation.