3.3: Parallel and Perpendicular Lines
3.8: Constructing Parallel and Perpendicular Lines
There is
is no
no spoon.
spoon.
There
-Spoon Boy and Neo
Relating Parallel and Perpendicular Lines
a
b
c
Theorem 3-9: If two lines are parallel to the same line, then
they are parallel to each other.
a || b

Relating Parallel and Perpendicular Lines
t
m
n
Theorem 3-10: In a plane, if two lines are perpendicular to the
same line, then they are parallel to each other.
m || n

Relating Parallel and Perpendicular Lines
t
m
1
2
n
Given : m  t, n  t
Prove : m || n
Statements
Reasons
1. m  t, n  t
1.
2. 1 and 2 are
right angles
2.
3. 1  2
3.
m || n
4.
4.
Relating Parallel and Perpendicular Lines
n
l
m
Theorem 3-11: In a plane, if a line is perpendicular to one of
two parallel lines, then it is also perpendicular to the other.
nm

Relating Parallel and Perpendicular Lines
n
1
l
2
Given : n  l, and l || m
Prove : n  m
Statements
Reasons
1. n  l, and l || m
1.
2. 1 is a right 
2.
3.
3. Corresp.  ‘s post.
4. n  m
4.
m
Constructing l || m
N
l
Given : Line l and point N not on l
Construct : line m through N with m || l
Step 1: Label point H on l. Draw HN. Label the angle it
makes with l as 1.
Step 2: Construct 2 with vertex at N so that 1  2
and thetwo angles are corresponding angles. Label this
line m.


Constructing a Special Quadrilateral
Given : Segments of length a and b
Construct : Quadrilateral ABYZ with
AZ  a, BY  b, and AZ || BY
a
b
Step 1: Construct AZ with length a.

Step 2: Draw a point B not on AZ. Then draw AB.
Step 3: Construct a ray parallel to AZ through B.
Step 4: Construct Y so that BY = b. Then draw YZ.

Constructing Perpendicular Lines
Given : Point P on line l
Construct : CP with CP  l
l
P
Step 1: Put the compass point on point P. Draw arcs
intersecting l in two points. Label the points A and B.
Step 2: Open the compass wider. With the compass tip
on A, draw an arc above point P.
Step 3: Without changing the compass setting, place the
compass point on B. Draw an arc that intersects the
previous arc and label the intersection C.
Step 4: Draw CP.
Constructing Perpendicular Lines
R
Given : line l and Point R not on l
Construct : RG with RG  l
l
Step 1: Put the compass point on point R. Draw arcs
intersecting l in two points. Label the points E and F.
Step 2: Place the compass point in E and make an arc.
Step 3: Without changing the compass setting, place the
compass point on F. Draw an arc that intersects the
previous arc and label the intersection G.
Step 4: Draw RG.
3.3: Parallel and Perpendicular Lines
3.8: Constructing Parallel and Perpendicular Lines
HOMEWORK: p. 140 #51-52, p. 144 #26-27, p. 153 #45-46,
Checkpoint Quiz 1 (p. 153) #1-9
Get
Get busy
busy living,
living, or
or get
get busy
busy dying.
dying.
-Red