EXHIBIT 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Registration Statements on Form S-8 (File Nos. 333-30514, 333-55798, 333-30516, 333-93729, 33-01297, 333-01297, 333-01299, 33-52044, 33-39680, 33-89528, 33-61485, 333-38629, 333-28495, 333-22169, 333-44701, 333-56287, 333-70227, 333-72783, 333-76027, 333-55800, 333-82914, 333-107292 and 333-113455) of Parametric Technology Corporation of our report dated December 7, 2004 relating to the consolidated financial statements, which appears in this Form 10-K.

/s/ PricewaterhouseCoopers LLP

Boston, Massachusetts

December 13, 2004