Quadrilateral
Figure
Definition
s
A closed plane figure consisting of four line segments.
A "crossed" (or "complex") quadrilateral has
one pair of intersecting sides.
A "concave" quadrilateral, pictured here, has one interior angle
greater than 180°.
The other possibility, described next, is "convex".
"
C
onvex" means every line segment connecting interior points is
entirely contained within the interior.
A convex quadrilateral with one pair of parallel sides.
A trapezoid with two opposite
sides parallel, the two other sides are of equal length.
This implies
that the two ends of each parallel side have equal angles, and that the
diagonals are of equal length.
A quadrilateral with two pairs of adjacent equal sides.
(In some text, a kit
e need not be convex; in
others concave kites are termed a "dart" or "arrowhead".)
A convex quadrilateral in which both pairs of opposite sides are parallel.
This implies
that opposite sides are of equal length, opposite angles are equal, and the di
agonals
bisect each other.
Each diagonal bisects the parallelogram into two congruent
triangles.
A convex quadrilateral with four right angles.
This implies
that opposite sides are parallel and
of equal length, and the diagonals bisect each other and
are equal in length.
A convex quadrilateral with all four sides of equal length.
This implies
that opposite sides
are parallel, opposite angles are equal, and the diagonals perpendicularly bisect each othe
r.
A convex quadrilateral with four side
s of equal length, and four right angles.
This implies
that
opposite sides are parallel, and that the diagonals perpendicularly bisect each other and are of equal
length.
Each diagonal bisects each pair of opposite angles
A quadrilateral with just on
e pair of congruent opposite sides, and just one pair of congruent
opposite angles is not necessarily a parallelogram.
The reason, can be seen by drawing the
shorter diagonal in the figure to the left, which divides the figure into two non

congruent
trian
gles which nonetheless have congruent side

side

angle (SSA).
Adjunct Displays
From book:
“
Adjunct displays appear outside of the text, such as pictures, geographic maps, concept maps, graphs, diagrams,
outlines, advance organizers, and so forth.
E
ffective displays reflect the
structure
of the information.
The graphic organizers given to students should be blank or partially completed.
For real learning to occur, students must use the graphic organizer to transform informatioin
Step

by

step
Select/
create an adjunct display that matches the concepts
Decide
if it will be blank partially completed with key words or phrases
Distribute the adjunct display and review it with students.
Inform students of the ultimate purpose of thea activity.
Allow stude
nts to complete the adjunct display with assisting as necessary.
Review as a class and transition students into transforming the information in oral or written form.
”
For my lesson plan:
Review the difference between polygons and non

polygons. Tell
class we will focus on the quadrilaterals today.
Draw the new adjunct display on the board. Pass out reading work sheet. Working in partners, allow students to
try to fill in t
he graphic organizer. Pass out quadrilaterals and labels. Have each studen
t tape at least one on the
board based on their classification. Discuss as a class why they organized it the way that they did. Would I
change anything? Form a consensus and finalize the chart.
Should appear like :
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