6.3 Showing Quadrilaterals are Parallelograms

Student Help
SKILLS REVIEW
To review the formula
for finding slope, see
p. 665.
Standardized Test
Practice
322 Chapter 6 Quadrilaterals
EXAMPLE Coordinate Geometry
Use the slopes of the segments in
the diagram to determine if the
quadrilateral is a parallelogram.
Solution
Lines and line segments are parallel
if they have the same slope.
Slope of AB&*: 4 0
2 1
4
4
1
0
Slope of DC &*: 4
6 5
4
A(1, 0) 4 D(5, 0) x
4
1
Slope of BC&*: 4 4
6 2
0
0
0 Slope of AD&*: 0
4 5 1
0
0
4
ANSWER The slopes of AB&* and DC &* are the same, so AB&* DC &*. The
slopes of BC&*and AD&* are the same, so AD&* BC&*. Both pairs
of opposite sides are parallel, so ABCD is a parallelogram.
1
y
B(2, 4) C(6, 4)
Coordinate Geometry Use the slopes of the segments in the
diagram to determine if the quadrilateral is a parallelogram.
25. y
26.
1
G(1, 4) H(5, 4)
F(2, 1)
1
J(6, 1)
27. Multi-Step Problem Suppose you shoot a pool ball as shown
below and it rolls back to where it started. The ball bounces off
each wall at the same angle at which it hits the wall.
a. The ball hits the first wall at an angle of 63.
So maAEF maBEH 63. Explain why maAFE 27.
b. Explain why maFGD 63.
c. What is maGHC? maEHB?
x
d. Find the measure of each interior angle of EFGH. What kind
of quadrilateral is EFGH? How do you know?
1
y
P(0, 2)
1
Œ(2, 5) R(5, 5)
S(4, 2)
x