Transcript Using Perpendicular and Parallel Lines
Section 3.6
Use properties of parallel and perpendicular lines.
None
10 Parallel Postulate 11 Perpendicular Postulate
3.11 & 3.12
Parallel Postulate- if there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
If P is not on l, then there exists one line m through P such that m
∥
l.
P
l m
Perpendicular Postulate- if there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
If P is not on l, then
m P
there exists one line m through P such that m
⊥
l.
l
The distance from a line to a point not on the line is the length of the segment
⊥
to the line from the point.
A All other distances are longer ⊥ Distance is the Shortest distance
• •
Perpendicular distance between a point and a line is the shortest distance in all cases.
When we say “distance”, we always mean “perpendicular or shortest distance”.
KITES Which segment shows the shortest distance from point A to DB?
A.
AD
B.
AB
C.
CX
D.
AX
If two lines are parallel to the same line, then they are parallel to each other.
If q
∥
r and r
∥
s, then q
∥
s.
r s q
Ladders were used to move from level to level of cliff dwellings. Each rung on the ladder is parallel to the rung immediately below it. Explain why
l
∥
p
.
l m n p
SOLUTION You are given that
l
∥
m
and
m
∥
n
. By Theorem
3.11
,
l
∥
n
. Since
l
∥
n
and
n
∥
p
, it follows that
l
∥
n
.
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
If m
⊥
p and n
⊥
p, then m
⊥
n.
m n p
Find the value of
x
that makes AB || CD .
SOLUTION By Theorem 3.12,
AB
and
CD
will be parallel If
AB
and
CD
are both perpendicular to
AC
. For this to be true
BAC
must measure
90 °
.
(2x + 2) = 90 °
m
BAC
must be 90° .
2x = 88
Subtract 2 from each side.
x = 44
Divide each side by 2 .
ANSWER If x = 44 , then AB || CD .
1.
Use the information in the diagram to explain why a ||
c
.
ANSWER a || b and b || c , so a || c (if two lines are parallel to the same line, then they are parallel to each other).
2.
Find a value of
x
so that d || e .
ANSWER 16
3)
Find the value of x that makes FG ││HJ
F H
ANSWER
x = 8 11x + 2 G J
Why did the Easter egg hide?
He was a little chicken!
What do you get if you cross rabbits and termites?
Bugs bunnies!
Why does a lobster never share?
Because it’s shellfish!
Section 3.6, pg. 147-149: #3-15 odd, 19, 21, 25, 27-31 odd