Download 8-3 Angle Relationships

8-5 Coordinate
Geometry
Objective: Students identify
polygons in the coordinate
plane.
Vocabulary
 Polygon-
is a closed plane figure formed
by three or more line segments called
sides.
 Quadrilaterals-
are polygons with four
sides and four angles.
Quadrilaterals
Trapezoids
Exactly 1 pair of
parallel sides
Parallelograms
2 pairs of parallel sides
Rectangles
Squares
4 right
4 congruent
angles
sides
4 congruent
angles
Rhombuses
4 congruent
sides
Slopes of Parallel and Perpendicular
Lines
 Any
two nonvertical lines with equal slopes are
parallel. Any two vertical lines are parallel.
 Any
two nonvertical lines whose slopes have a
product of -1 are perpendicular. Vertical and
horizontal lines are perpendicular.
Example 1
 Which
lines are parallel?
 Which lines are perpendicular?
Step 1 Find the slope of each line
Hint:
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
Slope of 𝑃𝑄=
X
Q
G
Slope of 𝑅𝑆=
Slope of 𝐴𝐵=
B
P
Slope of 𝑃𝐴=
H
Slope of 𝐺𝐻=
Slope of 𝑋𝑌=
Step 2 Compare the slopes
S
R
A
Y
Example 2
Graph the quadrilaterals with the given
vertices. Give all of the names that apply to
the quadrilateral.
J(1,2) K(4,2)
L(4,-1) M(1,-1)
P(-1,2) Q(2,1)
R(-1,-2) S(-3,0)
4
-1
6
-4
4
-4
Example 3
Find the coordinates of the missing vertex of
square ABCD with
A(4,0), B(0,4), and C(-4,0).
Step 1 Graph and connect the given
points
Step 2 Complete the figure to find the
missing vertex.
𝑨𝑩 has a slope of -1, so draw 𝑪𝑫 with
a slope of -1.
𝑩𝑪 has a slope of 1, so draw 𝑨𝑫 with a
slope of 1.
Where do the rays intersect?
4
-4
4
-4