Transcript Lesson 6, Parallel and Perpendicular Lines

Parallel and Perpendicular Lines
Geometry
Mrs. King
Unit 3, Lesson 6
Slope – Other Lines
Find the slope of PQ,
RS, and TU.
m of PQ  1
3
m of RS  1
3
m of TU 3
What can be said about
lines PQ and RS?
The lines are parallel and
have the same slope.
jwelker.lps.org/lessons/ppt/geod_3_3_slope.ppt
Slope – Parallel Lines
Parallel lines have equal slopes.
jwelker.lps.org/lessons/ppt/geod_3_3_slope.ppt
Line l1 contains P(0, 3) and Q(–2, 5). Line l2 contains
R(0, –7) and S(3, –10). Are lines l1 and l2 parallel?
Explain.
y2 – y1
x2 – x1
Slope of line l1 =
Slope of line l
2
=
y 2 – y1
x 2 – x1
=
=
5–3
–2 – 0
–10 –(–7)
3–0
= –22 = –1
=
–3
3
= –1
Each line has slope –1.
The lines have the same slope so they are parallel.
Are the lines y = –5x + 4 and x = –5y + 4 parallel?
Explain.
The equation y = –5x + 4 is in slope-intercept form.
Write the equation x = –5y + 4 in slope-intercept form.
x = –5y + 4
–
x – 4 = –5y
Subtract 4 from each side.
1
5
Divide each side by –5.
x+
4
5
=y
The line x = –5y + 4 has slope – 15 .
The line y = –5x + 4 has slope –5.
The lines are not parallel because their slopes
are not equal.
Slope – Other Lines
m of PQ  1
3
m of RS  1
3
m of TU 3
What can be said about
lines PQ and TU?
The lines are perpendicular
and have slopes which
multiply to -1.
jwelker.lps.org/lessons/ppt/geod_3_3_slope.ppt
Slope – Perpendicular Lines
Perpendicular lines have slopes which
are negative reciprocals of each other.
In other words, you have to FLIP and
NEGATE.
Line l1 contains M(0, 8) and N(4, –6). Line l2 contains
P(–2, 9) and Q(5, 7). Are lines l1 and l2 perpendicular?
Explain.
Find the slope of each line.
Lines l1 and l2 are not perpendicular because the slopes
are not negative reciprocals.
Theorem 2-5
Two lines parallel to a
third line are parallel
to each other.
Theorem 2-6
In a plane, two lines
perpendicular to a
third line are parallel
to each other.