<PAGE>
 
                                                                     EXHIBIT 3.5


                           PRENTISS PROPERTIES TRUST

ARTICLES SUPPLEMENTARY OF BOARD OF TRUSTEES CLASSIFYING AND DESIGNATING A SERIES
  OF PREFERRED SHARES OF BENEFICIAL INTEREST AS SERIES B CUMULATIVE REDEEMABLE
 PERPETUAL PREFERRED SHARES OF BENEFICIAL INTEREST AND FIXING DISTRIBUTION AND
                  OTHER PREFERENCES AND RIGHTS OF SUCH SHARES
                                        
          Prentiss Properties Trust, a Maryland real estate investment trust
(the "TRUST"), hereby certifies to the State Department of Assessments and
Taxation of Maryland pursuant to Section 8-203(b) of the Corporations and
Associations Article of the Annotated Code of Maryland that:

          FIRST:  Pursuant to the authority granted by the Amended and Restated
Declaration of Trust of the Trust filed with the Department on October 16, 1996
(the "DECLARATION"), the Board of Trustees of the Trust (the "BOARD OF
TRUSTEES"), by resolutions duly adopted on June 17, 1998, has designated and
classified 1,900,000 shares of the authorized but unissued and unclassified
preferred shares of beneficial interest, par value $.01 per share, of the Trust
as Series B Cumulative Redeemable Perpetual Preferred Shares of Beneficial
Interest, authorized the issuance of a maximum of 1,900,000 shares of such class
of Preferred Shares, and set the preferences, conversion and other rights,
voting powers, restrictions, limitations as to dividends, qualifications, terms
and conditions of redemption and other terms and conditions of such class of
Preferred Shares.

          SECOND:  The Series B Cumulative Redeemable Preferred Shares of
Beneficial Interest created by the resolutions duly adopted by the Board of
Trustees of the Trust referred to in Article FIRST of these Articles
Supplementary shall have the following designation, number of shares,
preferences, conversion and other rights, voting powers, restrictions and
limitation as to dividends, qualifications, terms and conditions of redemption
and other terms and conditions which, upon any restatement of the Declaration,
may be made a part of Article VI of the Declaration with any appropriate changes
in enumeration or lettering of any section or subsection thereof:

          SECTION 1.  DESIGNATION AND NUMBER.  A series of preferred shares of
beneficial interest, designated the "8.30% Series B Cumulative Redeemable
Perpetual Preferred Shares" (the "SERIES B PREFERRED SHARES") is hereby
established.  The number of shares of Series B Preferred Shares shall be
__________________, which number may be decreased (but not below the aggregate
number thereof then outstanding and which have been reserved for issuance) from
time to time by the Board of Trustees.

          SECTION 2.  RANK.  The Series B Preferred Shares will, with respect to
distributions or rights upon voluntary or involuntary liquidation, winding-up or
dissolution of the Trust, or both, rank senior to all classes or series of
Common Shares (as defined in the Declaration) and to all classes or series of
equity securities of the Trust now or hereafter authorized, issued or
outstanding, other than any class or series of equity securities of the Trust
<PAGE>
 
expressly designated as ranking on a parity with or senior to the Series B
Preferred Shares as to distributions or rights upon voluntary or involuntary
liquidation, winding-up or dissolution of the Trust, or both.  For purposes of
these Articles Supplementary, the term "PARITY PREFERRED SHARES" shall be used
to refer to any class or series of equity securities of the Trust now or
hereafter authorized, issued or outstanding expressly designated by the Trust to
rank on a parity with Series B Preferred Shares with respect to distributions or
rights upon voluntary or involuntary liquidation, winding-up or dissolution of
the Trust, or both, as the context may require, and includes the Series A
Cumulative Convertible Redeemable Preferred Shares of Beneficial Interest, par
value $.01 per share, of the Trust.  The term "equity securities" does not
include debt securities, which will rank senior to the Series B Preferred
Shares.

          SECTION 3.  DISTRIBUTIONS.  (a)  Payment of Distributions.  Subject to
the rights of holders of Parity Preferred Shares as to the payment of
distributions and holders of equity securities ranking senior to the Series B
Preferred Shares issued after the date hereof in accordance herewith as to
payment of distributions, holders of Series B Preferred Shares shall be entitled
to receive, when, as and if declared by the Board of Trustees of the Trust, out
of funds legally available for the payment of distributions, cumulative
preferential cash distributions at the rate per annum of 8.30% of the $50.00
liquidation preference per share of Series B Preferred Shares.  Such
distributions shall be cumulative and shall accrue from the first day of the
applicable Distribution Period (as defined herein), and will be payable (A)
quarterly in arrears, not later than the third calendar day after the end of the
applicable Distribution Period and, (B) in the event of a redemption, on the
redemption date (each a "PREFERRED SHARES DISTRIBUTION PAYMENT DATE").  For
purposes of these Articles Supplementary, the term "DISTRIBUTION PERIOD" shall
mean quarterly distribution periods commencing on January 1, April 1, July 1 and
October 1 of each year and ending on and including the day preceding the first
day of the next succeeding Distribution Period with respect to any Series B
Preferred Shares (other than the initial Distribution Period, which shall
commence on the original date of issuance for such Series B Preferred Shares and
end on and include the last day of the calendar quarter immediately following
the original date of issuance, and other than the Distribution Period during
which any Series B Preferred Shares shall be redeemed or exchanged, which shall
end on and include the date of such redemption or exchange).  The amount of the
distribution payable for any period will be computed on the basis of a 360-day
year of twelve 30-day months and for any period shorter than a full quarterly
period for which distributions are computed, the amount of the distribution
payable will be computed on the basis of the actual number of days elapsed in
such a 30-day month.  If any date on which distributions are to be made on the
Series B Preferred Shares is not a Business Day (as defined herein), then
payment of the distribution to be made on such date will be made on the next
succeeding day that is a Business Day (and without any interest or other payment
in respect of any such delay) except that, if such Business Day is in the next
succeeding calendar year, such payment shall be made on the immediately
preceding Business Day, in each case with the same force and effect as if made
on such date.  Distributions on the Series B Preferred Shares will be made to
the holders of record of the Series B Preferred Shares on the relevant record
dates to be fixed by the Board of Trustees of the Trust, which record dates
shall in no event exceed 15 Business Days prior to the relevant Preferred Shares
Distribution Payment Date (each a "DISTRIBUTION RECORD DATE").  Notwithstanding
anything to the contrary set forth herein, each share of Series B Preferred
Shares shall also continue to accrue all accrued and

                                       2
<PAGE>
 
unpaid distributions, whether or not declared, up to the exchange date on any
Series B Preference Unit (as defined in the Second Amendment to the Second
Amended and Restated Agreement of Limited Partnership of Prentiss Properties
Acquisition Partners, L.P., dated as of the date hereof, the "PARTNERSHIP
AGREEMENT") validly exchanged into such share of Series B Preferred Shares in
accordance with the provisions of such Partnership Agreement.

          The term "BUSINESS DAY" shall mean each day, other than a Saturday or
a Sunday, which is not a day on which banking institutions in New York, New York
are authorized or required by law, regulation or executive order to close.

          (b) Distributions Cumulative.  Distributions on the Series B Preferred
Shares will accrue and accumulate as of each Preferred Shares Distribution
Payment Date whether or not the terms and provisions of any agreement of the
Trust, including any agreement relating to its indebtedness at any time prohibit
the current payment of distributions, whether or not the Trust has earnings,
whether or not there are funds legally available for the payment of such
distributions and whether or not such distributions are authorized or declared.
Distributions on account of arrears for any past Distribution Periods may be
declared and paid at any time, without reference to a regular Preferred Shares
Distribution Payment Date to holders of record of the Series B Preferred Shares
on the record date fixed by the Board of Trustees which date shall not exceed 15
Business Days prior to the payment date.  Accumulated and unpaid distributions
will not bear interest.

          (c) Priority as to Distributions.  (i)  So long as any Series B
Preferred Shares are outstanding, no distribution of cash or other property
shall be authorized, declared, paid or set apart for payment on or with respect
to any class or series of Common Shares or any class or series of other shares
of beneficial interest of the Trust ranking junior as to the payment of
distributions to the Series B Preferred Shares (such Common Shares or other
junior shares of beneficial interest, collectively, "JUNIOR SHARES"), nor shall
any cash or other property be set aside for or applied to the purchase,
redemption or other acquisition for consideration of any Series B Preferred
Shares, any Parity Preferred Shares with respect to distributions or any Junior
Shares, unless, in each case, all distributions accumulated on all Series B
Preferred Shares and all classes and series of outstanding Parity Preferred
Shares as to payment of distributions have been paid in full.  The foregoing
sentence will not prohibit (i) distributions payable solely in Junior Shares,
(ii) the conversion of Series B Preferred Shares, Junior Shares or Parity
Preferred Shares into stock of the Trust ranking junior to the Series B
Preferred Shares as to distributions, (iii) purchase by the Trust of such Series
B Preferred Shares, Parity Preferred Shares with respect to distributions or
Junior Shares pursuant to Article VII of the Declaration to the extent required
to preserve the Trust's status as a real estate investment trust, and (iv) the
purchase, redemption or other acquisition of Common Shares made for the purpose
of an employee incentive or benefit plan of the Trust or any subsidiary.

          (ii) So long as distributions have not been paid in full (or a sum
sufficient for such full payment is not irrevocably deposited in trust for
payment) upon the Series B Preferred Shares, all distributions authorized and
declared on the Series B Preferred Shares and all classes or series of
outstanding Parity Preferred Shares with respect to distributions shall be

                                       3
<PAGE>
 
authorized and declared so that the amount of distributions authorized and
declared per share of Series B Preferred Shares and such other classes or series
of Parity Preferred Shares shall in all cases bear to each other the same ratio
that accrued distributions per share on the Series B Preferred Shares and such
other classes or series of Parity Preferred Shares (which shall not include any
accumulation in respect of unpaid distributions for prior distribution periods
if such class or series of Parity Preferred Shares do not have cumulative
distribution rights) bear to each other.

          (e) No Further Rights.  Holders of Series B Preferred Shares shall not
be entitled to any distributions, whether payable in cash, other property or
otherwise, in excess of the full cumulative distributions described herein.

          (f) No Declaration of Distributions.  No distributions on Series B
Preferred Shares shall be declared by the Board of Trustees or paid or set apart
for payment by the Trust at such time as the terms and provisions of any
agreement of the Trust (other than any agreement with a holder or Affiliate of a
holder of Equity Shares of the Trust), including any agreement relating to its
indebtedness, prohibits such declaration, payment or setting apart for payment
or provides that such declaration, payment or setting apart for payment would
constitute a breach thereof or a default thereunder, or if such declaration or
payment shall be restricted or prohibited by law. Nothing in this subsection (f)
shall be deemed to modify or affect in any manner the accrual provisions set
forth in Section 3(b) or the distribution priorities set forth in Section 3(c).

          (g) Determination of Distributions.  In determining whether a
distribution by dividend, redemption or other acquisition of Preferred Shares or
otherwise is permitted under Maryland law, no effect shall be given to amounts
that would be needed, if the Trust were to be dissolved at the time of the
distribution, to satisfy the preferential rights upon dissolution of
shareholders whose preferential rights on dissolution are superior to those
receiving the distribution.

          SECTION 4.  LIQUIDATION PREFERENCE.  (a)  Payment of Liquidating
Distributions.  Subject to the rights of holders of Parity Preferred Shares with
respect to rights upon any voluntary or involuntary liquidation, dissolution or
winding-up of the Trust and subject to equity securities ranking senior to the
Series B Preferred Shares with respect to rights upon any voluntary or
involuntary liquidation, dissolution or winding-up of the Trust, the holders of
Series B Preferred Shares shall be entitled to receive out of the assets of the
Trust legally available for distribution or the proceeds thereof, after payment
or provision for debts and other liabilities of the Trust, but before any
payment or distributions of the assets shall be made to holders of Common Shares
or any other class or series of shares of the Trust that ranks junior to the
Series B Preferred Shares as to rights upon liquidation, dissolution or winding-
up of the Trust, an amount equal to the sum of (i) a liquidation preference of
$50 per share of Series B Preferred Shares, and (ii) an amount equal to any
accumulated and unpaid distributions thereon, whether or not declared, to the
date of payment.  In the event that, upon such voluntary or involuntary
liquidation, dissolution or winding-up, there are insufficient assets to permit
full payment of liquidating distributions to the holders of Series B Preferred
Shares and any Parity Preferred Shares as to rights upon liquidation,
dissolution or winding-up of the Trust, all payments of

                                       4
<PAGE>
 
liquidating distributions on the Series B Preferred Shares and such Parity
Preferred Shares shall be made so that the payments on the Series B Preferred
Shares and such Parity Preferred Shares shall in all cases bear to each other
the same ratio that the respective rights of the Series B Preferred Shares and
such other Parity Preferred Shares (which shall not include any accumulation in
respect of unpaid distributions for prior distribution periods if such Parity
Preferred Shares do not have cumulative distribution rights) upon liquidation,
dissolution or winding-up of the Trust bear to each other.

          (b) Notice.  Written notice of any such voluntary or involuntary
liquidation, dissolution or winding-up of the Trust, stating the payment date or
dates when, and the place or places where, the amounts distributable in such
circumstances shall be payable, shall be given by (i) fax (if the holder of the
Series B Preferred Shares shall have provided the Trust with such holder's fax
number) and (ii) first class mail, postage pre-paid, not less than 30 and not
more that 60 days prior to the payment date stated therein, to each record
holder of the Series B Preferred Shares at the respective addresses of such
holders as the same shall appear on the share transfer records of the Trust.

          (c) No Further Rights.  After payment of the full amount of the
liquidating distributions to which they are entitled, the holders of Series B
Preferred Shares will have no right or claim to any of the remaining assets of
the Trust.

          (d) Consolidation, Merger or Certain Other Transactions.  The
voluntary sale, conveyance, lease, exchange or transfer (for cash, shares of
stock, securities or other consideration) of all or substantially all of the
property or assets of the Trust to, or the consolidation or merger or other
business combination of the Trust with or into, any corporation, trust or other
entity (or of any corporation, trust or other entity with or into the Trust) or
a statutory share exchange shall not be deemed to constitute a liquidation,
dissolution or winding-up of the Trust.

          SECTION 5.  OPTIONAL REDEMPTION.  (a)  Right of Optional Redemption.
The Series B Preferred Shares may not be redeemed prior to June 25, 2003.  On or
after such date, the Trust shall have the right to redeem the Series B Preferred
Shares, in whole or in part, at any time or from time to time out of funds
legally available therefor, upon not less than 30 nor more than 60 days' written
notice, at a redemption price, payable in cash, equal to $50 per share of Series
B Preferred Shares plus accumulated and unpaid distributions, whether or nor
declared, to the date of redemption.  If fewer than all of the outstanding
shares of Series B Preferred Shares are to be redeemed, the shares of Series B
Preferred Shares to be redeemed shall be selected pro rata (as nearly as
practicable without creating fractional shares).

          (b) Limitation on Redemption. (i)  The redemption price of the Series
B Preferred Shares (other than the portion thereof consisting of accumulated but
unpaid distributions) will be payable solely out of the sale proceeds of capital
stock of the Trust and from no other source.  For purposes of the preceding
sentence, "capital stock" means any equity securities (including Common Shares
and Preferred Shares), shares, participation or other

                                       5
<PAGE>
 
ownership interests (however designated) and any rights (other than debt
securities convertible into or exchangeable for equity securities) or options to
purchase any of the foregoing.

          (ii) The Trust may not redeem fewer than all of the outstanding shares
of Series B Preferred Shares unless all accumulated and unpaid distributions
have been paid on all outstanding Series B Preferred Shares for all quarterly
Distribution Periods terminating on or prior to the date of redemption.

          (c) Procedures for Redemption.  (i)  Notice of redemption will be (i)
faxed (if the holder of the Series B Preferred Shares shall have provided the
Trust with such holder's fax number) and (ii) mailed by the Trust, postage
prepaid, not less than 30 nor more than 60 days prior to the redemption date,
addressed to the respective holders of record of the Series B Preferred Shares
to be redeemed at their respective addresses as they appear on the transfer
records of the Trust.  No failure to give or defect in such notice shall affect
the validity of the proceedings for the redemption of any Series B Preferred
Shares except as to the holder to whom such notice was defective or not given.
In addition to any information required by law or by the applicable rules of any
exchange upon which the Series B Preferred Shares may be listed or admitted to
trading, each such notice shall state:  (i) the redemption date, (ii) the
redemption price, (iii) the number of shares of Series B Preferred Shares to be
redeemed, (iv) the place or places where such shares of Series B Preferred
Shares are to be surrendered for payment of the redemption price, (v) that
distributions on the Series B Preferred Shares to be redeemed will cease to
accumulate on such redemption date and (vi) that payment of the redemption price
and any accumulated and unpaid distributions will be made upon presentation and
surrender of such Series B Preferred Shares.  If fewer than all of the shares of
Series B Preferred Shares held by any holder are to be redeemed, the notice
mailed to such holder shall also specify the number of shares of Series B
Preferred Shares held by such holder to be redeemed.

          (ii) If the Trust gives a notice of redemption in respect of Series B
Preferred Shares (which notice will be irrevocable) then, by 12:00 noon, New
York City time, on the redemption date, the Trust will deposit irrevocably in
trust for the benefit of the Series B Preferred Shares being redeemed funds
sufficient to pay the applicable redemption price, plus any accumulated and
unpaid distributions, whether or not declared, if any, on such shares to the
date fixed for redemption, without interest, and will give irrevocable
instructions and authority to pay such redemption price and any accumulated and
unpaid distributions, if any, on such shares to the holders of the Series B
Preferred Shares upon surrender of the certificate evidencing the Series B
Preferred Shares by such holders at the place designated in the notice of
redemption.  If fewer than all Series B Preferred Shares evidenced by any
certificate is being redeemed, a new certificate shall be issued upon surrender
of the certificate evidencing all Series B Preferred Shares, evidencing the
unredeemed Series B Preferred Shares without cost to the holder thereof.  On and
after the date of redemption, distributions will cease to accumulate on the
Series B Preferred Shares or portions thereof called for redemption, unless the
Trust defaults in the payment thereof, such shares will no longer be deemed
outstanding, and all rights of the holders thereof as holders of Series B
Preferred Shares will cease (except the right to receive the redemption price
and any accrued and unpaid distributions upon surrender and endorsement of the
certificates evidencing the Series B Preferred Shares).  If any date fixed for
redemption of Series B Preferred Shares is

                                       6
<PAGE>
 
not a Business Day, then payment of the redemption price payable on such date
will be made on the next succeeding day that is a Business Bay (and without any
interest or other payment in respect of any such delay) except that, if such
Business Day falls in the next calendar year, such payment will be made on the
immediately preceding Business Day, in each case with the same force and effect
as if made on such date fixed for redemption. If payment of the redemption price
or any accumulated or unpaid distributions in respect of the Series B Preferred
Shares is improperly withheld or refused and not paid by the Trust,
distributions on such Series B Preferred Shares will continue to accumulate from
the original redemption date to the date of payment, in which case the actual
payment date will be considered the date fixed for redemption for purposes of
calculating the applicable redemption price and any accumulated and unpaid
distributions.

          (d) Status of Redeemed Shares.  Any Series B Preferred Shares that
shall at any time have been redeemed shall after such redemption, have the
status of authorized but unissued preferred shares of beneficial interest,
without designation as to class or series until such shares are once more
designated as part of a particular class or series by the Board of Trustees.

          (e) Shares-in-Trust.  Nothing in this Section 5 shall restrict the
Trust's right to purchase Shares-in-Trust pursuant to Article VII of the
Declaration.

          SECTION 6.  VOTING RIGHTS.  (a)  General.  Holders of the Series B
Preferred Shares will not have any voting rights, except as set forth below.

          (b) Right to Elect Trustees.  (i) If at any time distributions shall
be in arrears with respect to six (6) prior quarterly Distribution Periods
(including quarterly periods on the Series B Preferred Units prior to the
exchange into Series B Preferred Shares), whether or not consecutive, and shall
not have been paid in full (a "PREFERRED DISTRIBUTION DEFAULT"), the authorized
number of members of the Board of Trustees shall automatically be increased by
two and the holders of record of such Series B Preferred Shares, voting together
as a single class with the holders of each class or series of Parity Preferred
Shares upon which like voting rights have been conferred and are exercisable,
will be entitled to fill the vacancies so created by electing two additional
trustees to serve on the Trust's Board of Trustees (the "PREFERRED SHARES
TRUSTEES") at a special meeting called in accordance with SECTION 6(b)(ii) or at
the next annual meeting of stockholders, and at each subsequent annual meeting
of stockholders or special meeting held in place thereof, until all such
distributions in arrears and distributions for the current quarterly period on
the Series B Preferred Shares and each such class or series of Parity Preferred
Shares have been paid in full.

          (ii) At any time when such voting rights shall have vested, a proper
officer of the Trust shall call or cause to be called, upon written request of
holders of record of at least 10% of the outstanding Shares of Series B
Preferred Shares, a special meeting of the holders of Series B Preferred Shares
and all the series of Parity Preferred Shares upon which like voting rights have
been conferred and are exercisable (collectively, the "PARITY SECURITIES") by
mailing or causing to be mailed to such holders a notice of such special meeting
to be held not less than ten and not more than 45 days after the date such
notice is given.  The record date for determining holders of the Parity
Securities entitled to notice of and to vote at such special meeting will be the
close of

                                       7
<PAGE>
 
business on the third Business Day preceding the day on which such notice is
mailed. At any such special meeting, all of the holders of the Parity
Securities, by plurality vote, voting together as a single class without regard
to series will be entitled to elect two trustees on the basis of one vote per
$25.00 of liquidation preference to which such Parity Securities are entitled by
their terms (excluding amounts in respect of accumulated and unpaid dividends)
and not cumulatively. The holder or holders of a majority of the Parity
Securities then outstanding, present in person or by proxy, will constitute a
quorum for the election of the Preferred Shares Trustees except as otherwise
provided by law. Notice of all meetings at which holders of the Series B
Preferred Shares shall be entitled to vote will be given to such holders at
their addresses as they appear in the transfer records. At any such meeting or
adjournment thereof in the absence of a quorum, subject to the provisions of any
applicable law, a majority of the holders of the Parity Securities present in
person or by proxy shall have the power to adjourn the meeting for the election
of the Preferred Shares Trustees, without notice other than an announcement at
the meeting, until a quorum is present. If a Preferred Distribution Default
shall terminate after the notice of a special meeting has been given but before
such special meeting has been held, the Trust shall, as soon as practicable
after such termination, mail or cause to be mailed notice of such termination to
holders of the Series B Preferred Shares that would have been entitled to vote
at such special meeting.

          (iii) If and when all distributions in arrears and the distribution
for the current Distribution Period on the Series B Preferred Shares shall have
been paid in full or a sum sufficient for such payment is irrevocably deposited
in trust for payment, the holders of the Series B Preferred Shares shall be
divested of the voting rights set forth in SECTION 6(b) herein (subject to
revesting in the event of each and every Preferred Distribution Default) and, if
all distributions in arrears and the distributions for the current distribution
period have been paid in full or set aside for payment in full on all other
classes or series of Parity Preferred Shares upon which like voting rights have
been conferred and are exercisable, the term and office of each Preferred Shares
Trustee so elected shall terminate and the number of members of the Board of
Trustees shall be reduced accordingly.  Any Preferred Shares Trustee may be
removed at any time with or without cause by the vote of, and shall not be
removed otherwise than by the vote of, the holders of record of a majority of
the outstanding Parity Securities (including the Series B Preferred Shares when
they have the voting rights set forth in SECTION 6(b)) voting together as a
single class.  So long as a Preferred Distribution Default shall continue, any
vacancy in the office of a Preferred Shares Trustee may be filled by written
consent of the Preferred Shares Trustee remaining in office, or if none remains
in office, by a vote of the holders of record of a majority of the outstanding
Parity Securities (including the Series B Preferred Shares when they have the
voting rights set forth in SECTION 6(b)) voting together as a single class.  The
Preferred Shares Director shall each be entitled to one vote per trustee on any
matter.

          (c) Certain Voting Rights.  So long as any Series B Preferred Shares
are outstanding, the Trust shall not, without the affirmative vote of the
holders of at least two-thirds of the Series B Preferred Shares outstanding at
the time, (i) designate or create, or increase the authorized or issued amount
of, any class or series of shares ranking prior to the Series B Preferred Shares
with respect to payment of distributions or rights upon liquidation, dissolution
or winding-up or reclassify any authorized shares of the Trust into any such
shares, or create, authorize or issue any obligations or security convertible
into or evidencing the right to purchase

                                       8
<PAGE>
 
any such shares, (ii) issue to an affiliate of the Trust, or reclassifying any
authorized shares of the Trust held by an affiliate of the Trust, any Parity
Preferred Shares or any obligations or security convertible into or evidencing
the right to purchase any Parity Preferred Shares, or (iii) either (A)
consolidate, merge into or with, or convey, transfer or lease its assets
substantially as an entirety, to any corporation or other entity, or (B) amend,
alter or repeal the provisions of the Trust's Declaration (including these
Articles Supplementary) or By-laws, whether by merger, consolidation or
otherwise, in each case that would materially and adversely affect the powers,
special rights, preferences, privileges or voting power of the Series B
Preferred Shares or the holders thereof; provided, however, that with respect to
the occurrence of a merger, consolidation or a sale or lease of all of the
Trust's assets as an entirety, so long as (a) the Trust is the surviving entity
and the Series B Preferred Shares remain outstanding with the terms thereof
unchanged, or (b) the resulting, surviving or transferee entity is a
corporation, trust or other entity organized under the laws of any state and
substitutes the Series B Preferred Shares for other preferred stock having
substantially the same terms and same rights as the Series B Preferred Shares,
including with respect to distributions, voting rights and rights upon
liquidation, dissolution or winding-up, then the occurrence of any such event
shall not be deemed to materially and adversely affect such rights, preferences,
privileges or voting powers of the Series B Preferred Shares and the holders
thereof, and provided further that any increase in the amount of authorized
Preferred Shares or the creation or issuance of any other class or series of
Preferred Shares, or any increase in an amount of authorized shares of each
class or series, in each case ranking either (a) junior to the Series B
Preferred Shares with respect to payment of distributions and the distribution
of assets upon liquidation, dissolution or winding-up, or (b) on a parity with
the Series B Preferred Shares with respect to payment of distributions and the
distribution of assets upon liquidation, dissolution or winding-up, to the
extent such Preferred Shares are not issued to an affiliate of the Trust, shall
not be deemed to materially and adversely affect such rights, preferences,
privileges or voting powers.

          SECTION 7.  NO CONVERSION RIGHTS.  The holders of the Series B
Preferred Shares shall not have any rights to convert such shares into shares of
any other class or series of beneficial interest or into any other securities
of, or interest in, the Trust.

          SECTION 8.  NO SINKING FUND.  No sinking fund shall be established for
the retirement or redemption of Series B Preferred Shares.

          Section 9.  NO PREEMPTIVE RIGHTS.  No holder of the Series B Preferred
Shares of the Trust shall, as such holder, have any preemptive rights to
purchase or subscribe for additional shares of beneficial interest of the Trust
or any other security of the Trust which it may issue or sell.

          Section 10.  RECORD HOLDERS.  The Trust and the transfer agent for the
Series B Preferred Shares may deem and treat the record holder of any Series B
Preferred Shares as the true and lawful owner thereof for all purposes, and
neither the Trust nor the transfer agent shall be affected by any notice to the
contrary.

                                       9
<PAGE>
 
          THIRD:   The Series B Preferred Shares have been classified and
designated by the Board of Trustees under the authority contained in the
Declaration.

          FOURTH:  These Articles Supplementary have been approved by the Board
of Trustees in the manner and by the vote required by law.

          FIFTH:   The undersigned Vice President of the Trust acknowledges
these Articles Supplementary to be the corporate act of the Trust and, as to all
matters or facts required to be verified under oath, the undersigned Vice
President acknowledges that to the best of his knowledge, information and
belief, these matters and facts are true in all material respects and that this
statement is made under the penalties for perjury.

                                       10
<PAGE>
 
          IN WITNESS WHEREOF, the Trust has caused these Articles Supplementary
to be executed under seal in its name and on its behalf by its Vice President
and attested to by its Secretary on this 25th day of June, 1998.

                                    PRENTISS PROPERTIES TRUST


                                    By: /s/ MICHAEL A. ERNST
                                       -----------------------------
                                       Michael A. Ernst
                                       Senior Vice President



     ATTEST:

     GREGORY S. IMHOFF
     ---------------------------
     Gregory S. Imhoff
     Secretary

                                       11