Transcript Classifying Quadrilaterals_advanced

Classifying
Quadrilaterals
“…geometric shapes are the
alphabet in which the book of
nature is written." -Galileo
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Objectives
 Define what parallelograms, kites,
rectangles, squares, rhombi, and
trapezoids are.
 Sort and classify quadrilaterals.
 Determine which shapes are and are
not quadrilaterals, given examples.
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What is a Quadrilateral?
A. A quadrilateral is a two-dimensional figure
formed by connecting four segments endpoint to
endpoint with each segment intersecting exactly
two others. It also has four sides and four
angles.
B. A four sided polygon.
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Types of Quadrilaterals
 Trapezoid
 Parallelogram
 Square
 Rectangle
 Kite, Dart
Which one is
NOT a
quadrilateral?
 Rhombus
 Scalene
 Rectangle
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Classification of Quadrilaterals
 A concave
quadrilateral
contains at least one
angle that is >180o.
 A quadrilateral is
convex if each
vertex lies in the
interior of the
opposite angle.
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Name that Quadrilateral!
(No points for this name!)
 A square is a
quadrilateral with
all sides and
angles equal.
 If all quadrilaterals
have 360o total,
what is the angle
of each vertex in
a square?
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Name that Quadrilateral!
 A quadrilateral with
all angles equal is a
rectangle.
 A quadrilateral with
all sides equal is a
rhombus.
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In Euclidean geometry, a rhombus or rhomb is a
convex quadrilateral whose four sides all have the
same length. The rhombus is often called a diamond,
after the diamonds suit in playing cards, or a
lozenge, though the latter sometimes refers
specifically to a rhombus with a 45° angle.
Every rhombus is a parallelogram, and a rhombus with
right angles is a square. (Euclid's original
definition and some English dictionaries' definition
of rhombus excludes squares, but modern
mathematicians prefer the inclusive definition.)[1]
The English word “rhombus” derives from the Ancient
Greek ῥόμβος (rhombos), meaning spinning top. The
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plural of rhombus can be either rhombi or rhombuses.
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Name that Quadrilateral!
Trapezoid
 A quadrilateral with at least one pair of
parallel sides is a t……oid.
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Name that Quadrilateral!
 A quadrilateral with both
pairs of opposite sides
parallel and equal in
length is known as a
p….gram.
 Parallelograms can be considered special cases
of trapezoids, since they have a least one pair
of parallel sides.
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Name that Quadrilateral!
 A quadrilateral
with two separate
pairs of equal
adjacent sides is
commonly called
a ????.
 However, if the
kite is concave, a
dart is a more
appropriate term.
 This is a dart:
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Are They Quadrilaterals?
A
B
C
 Examples of shapes or curves that are
not classified as quadrilaterals. They do
not follow the definition of a quadrilateral.
Can you give a reason why?
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LO:To classify quadrilaterals
A
I need more practice to help me understand
this and I made lots of mistakes.
B
I am beginning to understand this
and I got many of them correct.
C
I really understand this and
I got most of them correct.
Follow up activity
Work in pairs.
You will be given the name of
a shape.
For each shape, you must write as many facts as you can
that are true about the shape in your book.
For example you can say that a scalene triangle has three
sides. You can not say that it does not have four sides.
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