Download Squares and Rectangles

Squares and Rectangles
A presentation by Ms. Stupp’s
favorite students :
Juliana Berhane
Tiffany Jeong
& Alex Gentile
Rectangles
Rectangles are parallelograms with four right angles. In short,
they have four perpendicular segments making their sides.
A rectangles diagonals bisect each other.
A shape is a rectangle if and only if its diagonals are congruent.
If a parallelogram has one right angle, then it is a rectangle.
The Golden Rectangle
The Golden rectangle is a very special
rectangle. It is a rectangle whose
lengths and widths are proportional to
the Golden Ratio.
The Golden ratio (also known as the
divine proportion) is 2 : 1 + radical 5.
Throughout the ages, these rectangles
have been used in architecture for
their pleasing appearance to the eye.
An Oblong
A rectangle that is not a square is colloquially known as an
oblong.
The term 'oblong' is generally not used today in
mathematics. However, it is occasionally used to mean a
rectangle whose sides are not equal. In other words,
"rectangle" is a generic term for a quadrilateral with four right
angles, subdivided into two categories:
squares: equal-sided rectangles
oblongs: non-equal-sided rectangles
The word oblong was once commonly used as an alternate
name for a rectangle. In his translation of Euclid’s Elements,
Sir Thomas Heath translates the Greek word ετερομηκες
[hetero mekes – literally, "different lengths"] in Book One,
Definition 22 as oblong. "Of Quadrilateral figures, a square is
that which is both equilateral and right-angled; an oblong that
which is right angled but not equilateral...".
Rectangle (Look at chart)
Each pair of opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Diagonals bisect each other
Diagonals are not perpendicular
Diagonals are congruent
Diagonals do not bisect two angles
Base angles are congruent
Squares
A square is both a rectangle & a rhombus,
therefore it can have two definitions:
A square is an equiangular rhombus.
A square is an equilateral rectangle.
Along with these definitions, a square is a
parallelogram as well.
Square Facts
In plane (Euclidean) geometry, a square is a polygon with
four equal sides, four right angles, and parallel opposite
sides.
The perimeter of a square whose sides have length s is
P = 4s
And the area is
A = s2
In classical times, the second power was described in terms
of the area of a square, as in the above formula. This led to
the use of the term “square” to mean raising to the second
power.
Each angle in a square is equal to 90 degrees, or a right
angle.
The diagonals of a square are equal. Conversely, if the
diagonals of a rhombus are equal, then that rhombus must
be a square. The diagonals of a square are about 1.41 times
the length of a side of the square. This value, known as
Pythagoras’ constant, was the first number proven to be
irrational.
More Square Facts
If a circle is circumscribed around a square, the area of the
circle is about 1.57 times the area of the square.
If a circle is inscribed in the square, the area of the circle is
about 0.79 times the area of the square.
A square has a larger area than any other quadrilateral with
the same perimeter.
The square is a highly symmetric object. There are four lines
of reflectional symmetry and it has rotational symmetry
through 90°, 180° and 270°. Its symmetry group is the
dihedral group D4.
If the area of a given square with side length S is multiplied
by the area of a "unit triangle" (an equilateral triangle with
side length of 1 unit), which is
/4 units squared, the new
area is that of the equilateral triangle with side length S.
Squares (Look at chart)
Each pair of opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Diagonals bisect each other
Diagonals are perpendicular
Diagonals are congruent
Diagonals bisect two angles
Base angles are congruent
Squares and Rectangles
You see squares
and rectangles
everywhere
you go . . .
Buildings
Electronics
Spongebob
That’s our show!
Now turn your attention to the
overhead and answer our questions!