Download The diagonals are congruent.

Notes: QUADRILATERALS ON A COORDINATE PLANE
For items a – k, check the box if the property is true for each classification of parallelograms.
CLASSIFICATION
PROPERTIES
a.
The opposite sides are parallel.
b.
The opposite sides are congruent.
c.
The opposite angles are congruent.
d.
The consecutive angles are supplementary.
e.
The diagonals bisect each other
f.
It has four right angles
g.
The diagonals are congruent.
i.
It has four congruent sides
j.
The diagonals are perpendicular.
k.
The diagonals bisect opposite angles.
RECTANGLES
RHOMBI
SQUARES
For #1 – 2, refer to the table completed properties above.
1. What do you know about the angles of ALL parallelograms?
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______________________________________________________________________________________________
2. What do you know about the sides of ALL parallelograms?
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Geometry Unit 7- Properties of Polygons
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Notes: QUADRILATERALS ON A COORDINATE PLANE
TERM
DESCRIPTION
EXAMPLE
HOW TO
NAME IT
Two coplanar lines that never __________
and have the _________ slope.
l ||m
Two lines that intersect to form four
__________ angles and have slopes
that are ____________ ____________.
l m
Slope is RISE over RUN.
EXAMPLE 1: Determine if quadrilateral ABCD is a parallelogram by proving whether or not both
pairs of opposite sides are parallel.
Slope of AB : _________
Slope of DC : _________
Parallel?
Yes
or
No
Slope of BC : _________
Slope of AD : _________
Parallel?
Yes
or
No
How do you know if the opposite sides are congruent?
______________________________________________________________________
______________________________________________________________________
Is quadrilateral ABCD is a parallelogram?
Yes
or
No
How do you know? _____________________________________________________
____________________________________________________________________
Geometry Unit 7- Properties of Polygons
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Notes: QUADRILATERALS ON A COORDINATE PLANE
EXAMPLE 2: Determine the most specific classification of parallelogram ABCD.
Slope of AB : _________
Slope of CB : _________
Perpendicular?
Yes
or
No
or
No
or
No
Slope of DC : _________
Slope of DA : _________
Perpendicular?
Yes
Slope of CA : _________
Slope of DB : _________
Perpendicular?
Yes
How do you know if the opposite sides are congruent?
______________________________________________________________________
______________________________________________________________________
How do you know if the diagonals are congruent?
______________________________________________________________________
______________________________________________________________________
What is the most specific classification of parallelogram ABCD? __________________
How do you know? _____________________________________________________
_____________________________________________________________________
Geometry Unit 7- Properties of Polygons
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Notes: QUADRILATERALS ON A COORDINATE PLANE
The two-dimensional coordinate system has four quadrants:
Quadrant I: (positive, positive)
Quadrant II: (negative, positive)
Quadrant III: (negative, negative)
Quadrant IV: (positive, negative)
II I
III IV
EXAMPLE 3: Plot the parallelogram as described.
Three vertices of a parallelogram have coordinates
(1, -1), (3, 8) and (5, 0). What are the coordinates
of the second-quadrant vertex?
( ______ , ______ )
QUICK CHECK: Plot the parallelogram as described.
Three vertices of a parallelogram have coordinates
(0, 1), (3, 7) and (4, 4). What are the coordinates of the
fourth-quadrant vertex?
( ______ , ______ )
Geometry Unit 7- Properties of Polygons
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Notes: QUADRILATERALS ON A COORDINATE PLANE
For items a – e, check the box if the property is true for each classification of quadrilaterals.
CLASSIFICATION
PROPERTIES
a.
It has exactly one pair of parallel sides.
b.
The median is equal to ½ (b1 + b2).
c.
The legs are congruent.
d.
The diagonals are congruent.
e.
The base angles are congruent.
TRAPEZOID
ISOSCELES
TRAPEZOID
EXAMPLE 4: A portion of isosceles trapezoid WXYZ
X
is shown on the grid. At what
coordinates should vertex Z be placed to
make XY parallel to WZ?
W
Y
Slope of XY : _________
Length of WX : _________
Z (_____ , _____)
QUICK CHECK: Which of the following points will complete
isosceles trapezoid QRPN?
A.
R (-2, 3)
B.
R (0, 4)
C.
R (2, 7)
D.
R (4, 9)
Geometry Unit 7- Properties of Polygons
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Notes: QUADRILATERALS ON A COORDINATE PLANE
The slope-intercept equation of a line is y = mx + b.
EXAMPLE 5: Determine the equations of the line that will contain AB in each of the figures.
a.
c.
C
D
D
B
C
A
A
B
y = ______________________
b.
y = ______________________
d.
B
C
A
D
C
D
A
B
y = ______________________
Geometry Unit 7- Properties of Polygons
y = ______________________
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