Day 6 – Parallel, Perpendicular Lines, Perpendicular Bisectors
Parallel Lines:
Perpendicular Lines:
Skew Lines:
Parallel planes:
Ex.
Given the diagram to the right, identify:
a. a pair of parallel segments
b. a pair of skew segments
c. a pair of perpendicular segments
d. a pair of parallel planes
Slopes of Parallel and Perpendicular Lines (Algebra Review)
If two lines are parallel, their slopes are
.
If two lines are perpendicular, their slopes are
Ex.
.
Use the slopes to determine if the segments with the given endpoints are parallel,
perpendicular, or neither. Show work that verifies your answer.
y
10
8
GH and IJ , given that G(-3,-2) H(1,2) I(-2,4) J(2,-4)
6
4
2
–10
–8
–6
–4
–2
2
–2
–4
–6
–8
–10
4
6
8
10
x
Day 6 – Parallel, Perpendicular Lines, Perpendicular Bisectors
Perpendicular bisector:
B
A
Write the Parallel Postulate on your Postulate Sheet.
Constructions
Construct the line parallel to the line, through the given point.
C
A
B
Construct the perpendicular bisector of the segment. (This also allows you to construct a
midpoint.)
B
A
Construct the line perpendicular to the given line, through the given point.
C
A
B
Day 6 – Parallel, Perpendicular Lines, Perpendicular Bisectors
Homework:
1. Given the diagram to the right, identify:
a. a pair of parallel segments
b. a pair of skew segments
c. a pair of perpendicular segments
d. a pair of parallel planes
2. Use the slopes to determine if the segments with the given endpoints are parallel,
perpendicular, or neither. Show work that verifies your answer.
a. HJ and KM with H(3,2) J(4,1) K(-2,4) M(-1,-5)
c. QR and ST with Q(6,1) R(-2,4)
S(5,3) T(-3,-1)
y
–8
–6
–4
y
8
8
6
6
4
4
2
2
–2
2
4
6
8
x
–8
–6
–4
–2
2
–2
–2
–4
–4
–6
–6
–8
–8
b. LM and NP with L(-2,2) M(2,5) N(3,6) P(3,-2)
4
6
8
x
d. AB and AC with A(-4,5) B(1,5) C(-4,-6)
y
y
8
8
6
6
4
4
2
2
–8
–8
–6
–4
–2
2
–2
–4
–6
–8
4
6
8
x
–6
–4
–2
2
–2
–4
–6
–8
4
6
8
x
Day 6 – Parallel, Perpendicular Lines, Perpendicular Bisectors
3. Construct the following.
C
A
a. A line parallel to the given line, through the given point.
Y
X
Z
B
b. The perpendicular bisector of the segment
YY
XX
Z
F
E
D
G
B
c. The line perpendicular to the given line, through the given point.
F
A
C
Y
G
X
Z
B