Describe the relatinship between different quadrilateralsin this hierarcy. Explain your answer. a. What is the relationships between a (1) quadrilateral, (2) kite, (3) rhombus, and (4) square? is a square a rhombus, is a rhombus a kite, is a kite a quadrilateral? Explain. b. What is the relationship between a (1) quaddrilateral, (2) trapezoid, (3) isoscles trapezoid, (4) rectangle, and (5) square? Is a square a rectangle, is a rectangle an isosceles trapezoid, is an isosceles trapezoid a trapezoid, is a trapezoid a quadrilateral? Explain. c. How do parellelograms fit into the mix? Solution a. It depends on how exactly you definite a \"kite\". Formally speaking, your teacher is wrong. A kite is typically defined as a planar, convex quadrilateral where two adjacent sides are of the same length as each other (\"a\"), and the other two adjacent sides are of the same length as each other (\"b\"): http://mathworld.wolfram.com/Kite.html So in this sense, a rhombus is a type of kite (where a=b), and a square is a type of kite too (where a=b, and there\'s a 90 degree angle). I\'m guessing that your teacher is redefining \"kite\" to be such a shape where \'a\' and \'b\' are strictly NOT equal to each other, or some equivalent of that. In that case, your teacher is correct. But this confusion is why it\'s important to have formal definitions in mathematics. 2. 1) THREE QUADRILATERALS: Square...Rectangle..trapezoid...Rhombus 2) PROPERTIES OF PARALLELOGRAM: - All sides across from each other are parallel - Diagonals bisect each other - opposite sides are congruent - opposite angles are congruent 3)TWO METHODS THAT PROVE IT IS A P.GRAM: -If pairs of opposite sides are congruent - if consecutive angles are supplementary 4) DIFFERENCE BETWEEN TRAPEZOID AND ISOSCELES TRAPEZOID: - Trapezoid has one pair of parallel sides and one pair of congruent sides - Isosceles Trapezoid also has a pair of parallel sides but the other pair of sides are not congruent 5)KINDS OF ANGLES THAT ARE FORMED BY DIAGONALS OF A.. - Kite -Diagonals are perpendicular -Square -diagonals are perpendicular -Rhombus -diagonals are perpendicular 3..

1. Describe the relationship between a corporation’s common stockholders, its board of directors,
and its chief executive officer (CEO)
Solution
Roles of Shareholders and Directors
A. Separating the Shareholder Roles and Director Roles
With Angels and venture capital investors assuming active participation in company
management, there is often some confusion about the respective roles of directors, shareholders,
and management.
The role of directors is one of stewardship. Directors are responsible for managing or, under
some statutes, supervising the management of, the corporation. If the Board of Directors is
dissatisfied with company management, its recourse is through the company's CEO. If the CEO
is not performing as expected, the Board may replace him.
Shareholders make a financial investment in the corporation, which entitles those with voting
shares to elect the directors. Shareholders do not normally have any rights to be involved directly
in company management. Their connection to company management is typically via the Board
of Directors as described above. If shareholders are not satisfied with the performance of the
directors, they may remove the directors or refuse to re-elect them.
Except for certain fundamental transactions or changes, shareholders normally do not participate
directly in corporate decision-making and while, as a practical matter, boards want to know the
views of the shareholders, strictly speaking, directors are not normally required to solicit or
comply with the wishes of shareholders.
C. Duties of Directors
A director's duty is owed first and foremost to the corporation. This duty is grounded in basic
principles of good faith, stewardship and accountability. Requirements imposed both by common
law and various statutes seek to establish the parameters of this duty without limiting the
flexibility of these principles.
1. To Whom are Directors Accountable?
Directors are required by corporate statutes to discharge their duties “with a view to the best
interests of the corporation.” Traditionally, this phrase has been interpreted to extend only to the
“shareholders as a whole.” However, in reaching their decisions, directors are often confronted
with a number of competing interests. In recent years, some courts have been prepared to give
directors more scope in considering the interests of different persons affected by corporate acts
without encroaching on the principle of acting in the corporation's best interests.

2. The courts recognize that acting with a view to the best interests of the corporation does not
mean that directors must disregard the interests of “stakeholders” such as employees, creditors,
and the community or country in which the corporation carries on business who may be affected
by the actions of the corporation. Considering these interests is often in the long-term best
interests of the corporation. Nevertheless, no court has ever recognized a duty to such
stakeholders.
2. Directors Duty to the Interests of the Shareholders
Courts have held that directors owe a duty to the corporation and not its individual shareholders.
In many instances, the distinction is not significant, since what is good for the corporation will
also benefit its shareholders. Maximizing the return to shareholders is also, in many cases,
consistent with the best interests of the corporation.
Nevertheless, there may be instances where the interests of the corporation and its particular
shareholders or classes of shareholders diverge. The interests of the common shareholders may
lie in realizing a short-term gain on their investment, a goal which the directors may conclude is
not necessarily in the long-term best interests of the corporation.
Additionally, the interests of majority shareholders may not be the same as the interests of the
corporation. A controlling shareholder may want the corporation to take certain action that may
be in its interest, but not necessarily in the best interests of the corporation. The right solution to
these kinds of issues depends very much on the facts of each situation.
3. Directors Duty to the Interests of Other Stakeholders
Directors recognize that their decisions have an impact beyond the corporation and its
shareholders. Employees and the community will be affected by a decision to close a plant.
Debenture holders may be affected by high-risk business strategies or by corporate
reorganizations. The national interest may be affected by a decision to move operations offshore.
Directors may feel a responsibility to consider the interests of these stakeholders.
The modern interpretation of a director's duty to the corporation permits directors to consider
these interests in coming to a decision about what is in the best interests of the corporation.
If today the directors of a company were to consider the interests of its employees, no one would
argue that in doing so they were not acting bona fide in the interests of the company itself.
Similarly, if the directors were to consider the consequences to the community of any policy that
the company intended to pursue, and were deflected in their commitment to that policy as a
result, it could not be said that they had not considered bona fide the interests of the
shareholders.
Certain American jurisdictions have statutes permitting directors to consider interests other than
those of the corporation or the shareholders as a whole. Some states permit (and, in
circumstances such as take-over bids, require) directors to consider the interests of employees,

3. suppliers, creditors and consumers. Some states include local and national economies and society
as a whole in the interests to be considered. Such legislation was enacted in the wake of high
levels of take-over activity in the 1980s (particularly by non-Americans) and was, at least in part,
a response to decisions facing boards of directors that had significant implications for
stakeholders of the corporation other than shareholders. These state statutes have been the
subject of extensive criticism and in some states have been repealed.
D. Directors' Conflict of Interest
Directors may have a number of relationships that will put them in a position of conflict or give
rise to an obligation to disclose details of a relationship.
1. When Does a Conflict Arise?
Directors who have an interest in a contract or proposed contract (e.g. a term sheet) with the
corporation must consider the matter carefully. If the contract is material from the corporation's
perspective, the directors will be under a statutory obligation to declare their interest and, with
some exceptions, to refrain from voting on the matter.
Voting on a matter in these circumstances would constitute a breach of their fiduciary obligation
to act in the best interests of the corporation. Under the corporate statutes, directors have an
interest in a contract not only if they themselves are a party to the contract, but also if they have a
material interest in any person who is a party to the contract.
The statutes do not define when a director has a material interest in a person, but material interest
is generally interpreted to mean an interest that is sufficient to result in some benefit to the
director.
Directors who are also substantial shareholders of the corporation are not automatically in a
position of conflict. Such directors must, however, separate their role as directors from their
interests as shareholders. In voting on matters in their capacity as shareholders, those directors
may, of course, vote without regard for the interests of other shareholders. In voting as directors,
however, they must still act in the best interests of the corporation in respect of any matter before
them.
The corporate statutes require directors to disclose in writing to the corporation their interest in
any material contract or to request that the interest be entered in the minutes of a meeting of the
board.
Whether the contract is material will be determined with reference to the materiality threshold of
the corporation.
The nature of a director's interest must be disclosed in sufficient detail to allow the other
directors to understand what the interest is and how far it goes. A director's interest must also be
disclosed within the timeframe prescribed by the relevant corporate statute.
2. Voting and Abstaining from Voting

4. Directors cannot normally vote on a contract in which they have a material interest. There are
exceptions for contracts that involve the directors' remuneration or an indemnity in which they
have an interest. Exceptions are also made if the contract in question relates to security for
money lent to the director or obligations undertaken by the director for the benefit of the
corporation or if it relates to an affiliate of the corporation. As a result of this last exception,
directors who serve on boards of affiliated corporations are not required to refrain from voting on
contracts between the two corporations that they serve.
Two results may flow from a director's failure to disclose an interest in a material contract or, in
some cases, from voting when not entitled to do so. First, the director may be required to account
to the corporation or its shareholders for any gain or profit realized from the contract. Second,
the corporation, its shareholders or, in some cases, securities regulators, may apply to the court to
have the contract set aside. Under some statutes, the director may nevertheless avoid these results
if the contract is confirmed or approved by special resolution of the shareholders after
appropriate disclosure of the director's interest in the contract. If the director failed to make the
necessary disclosure and the contract was not reasonable and fair to the corporation at the time it
was approved by the shareholders, there is no protection for the director under the corporate
statute.
Directors should be aware that the specific provisions in the corporate statutes dealing with a
director who is in a position of conflict apply only in relatively limited circumstances. They
apply only to certain contracts or proposed contracts with the corporation and would, arguably,
not include litigation, for example. Further, these provisions apply only to contracts that are
material to the corporation, not to contracts that do not meet this threshold.
In practice, however, most directors apply the rules broadly. They do not confine the restrictions
to the statutory requirements, but concern themselves with the issue of perceived, and actual,
conflict and what seems to be the right thing to do. In practice, directors will take themselves
completely out of the consideration of a particular matter where there may be a perception of
conflict or a perception that they may not bring objective judgment to the consideration of the
matter. In appropriate circumstances, directors will declare their position and absent themselves
not only from the vote, but also the discussion. However, directors should be aware that
abstaining from voting, except in certain limited circumstances, may not protect them from
liability under the corporate statutes. In particularly difficult situations, it may be necessary or
appropriate for a director to resign.
E. Reviewing the Role of Shareholders
1. General
The directors and not the shareholders are responsible for the management of the corporation.
However, under the corporate statutes, certain matters are considered so fundamental that they

5. require the approval of the shareholders. Under the Canada Business Corporations Act these
matters include:
Effecting certain amalgamations or reorganizations;
Selling all or substantially all of the corporation's assets;
Adding or removing any restrictions on the business that the corporation may carry on;
Changing the corporation's share capital;
Increasing or decreasing the number of directors or the minimum or maximum numbers of
directors;
Confirming by-laws; and,
Adding or changing restrictions on the issue, transfer or ownership of shares.
If a fundamental change affects holders of certain series of classes of shares differently than
others, the change must also be approved by a majority of the series or class of shares whose
existing rights may be affected by the change, whether or not the shares otherwise carry voting
rights.
As noted above, public corporations must also comply with the requirements of the provincial
securities commissions and the stock exchanges which impose requirements for shareholder
approval.
Finally, there may be issues which the directors determine should be put to the shareholders as a
matter of good corporate governance, whether or not they are legally required to do so. The issue
of whether shareholder approval was necessary to put a shareholder rights plan in place was
commonly debated when shareholder rights plans first came into use in Canada. A number of
boards of directors determined that the advice of the shareholders through a shareholders' vote
was essential well before the view of the regulators to the same effect was known. Similar
considerations will certainly arise in the future in the context of other decisions facing public
companies.
2. Shareholder Ability to Change the Board
Shareholders who are dissatisfied with how the directors are running the corporation may
remove the directors or refuse to re-elect them. In practice, this may be a difficult course to take,
particularly where the shares of the corporation are widely held.
Although the corporate statutes require a corporation to provide a list of shareholders to any
shareholder who requests it, thereby enabling shareholders to mount a proxy battle over the
election of directors, many shareholders do not have the time or resources required to counter a
management proposal. The exceptions are large institutional investors who have, on occasion,
made their voices heard at annual meetings or in private meetings with representatives of a
corporation prior to a shareholder meeting.
Occasionally, proxy battles do occur which result in the replacement of the board of directors.

6. 1Note: Especially in private companies involving venture capital investment, it is not uncommon
for certain decisions that are normally made by the Board of Directors to require venture capital
investor approval. A common example are key management decisions and financing decisions.