Transcript Q - Images

Geometry 3.1: Relationships
Between Lines
Parallel lines: Coplanar lines that never
intersect (they will go in the same
direction).
Symbols:
B
C
A
D
F
G
Ex: AB || DC
E
H
Perpendicular Lines: Intersect at a right
angle.
Symbols:
B
Ex: AB AE
C
A
D
F
E
G
H
Skew Lines: Noncoplanar lines that do
not intersect (they will go in different
directions)
Ex: AB and DH
B
C
A
D
F
E
G
H
CAREFUL!
c
a
b
Remember to visualize in 3D!
Line c intersects line b, but
lines a and c are skew.
Parallel Planes: planes in the same
direction that will not intersect
Ex: Plane ABC and
Plane FEH
B
C
A
D
F
E
G
H
1) Name all segments parallel to QX.
NE, MH, TO, SG, RA
N
M
E
H
Q
T
X
O
R
S
G
A
1) Name all segments parallel to QX.
NE, MH, TO, SG, RA
N
M
2) Name all planes that
intersect plane MHE.
E
H
Planes MNQ
MHT
HEX
Q
T
X
O
NEX
R
S
G
A
1) Name all segments parallel to QX.
NE, MH, TO, SG, RA
2) Name all planes that
intersect plane MHE.
Planes MNQ
MHT
HEX
NEX
3) Name all segments
parallel to QR.
XA
N
M
E
H
Q
T
X
O
MT
HO
R
S
G
A
1) Name all segments parallel to QX.
NE, MH, TO, SG, RA
2) Name all planes that
intersect plane MHE.
Planes MNQ
MHT
HEX
NEX
3) Name all segments
parallel to QR.
N
M
E
H
Q
T
XA, MT, HO
4) Name all segments skew to AG.
X
O
TO, MH, NE, XQ
TS, MT, NQ, QR
R
S
G
A
Transversal
• A line that intersects 2 or more coplanar
lines at different points.
• Ex:
• Nonexample:
Does not
intersect the two
lines at two
different points!
Corresponding Angles
• 2 angles in
corresponding positions
(same side of transversal,
same respective side of
lines)
Alternate Interior Angles
• 2 angles between the
two lines on opposite
sides of transversal
Same-Side Interior Angles
(aka consecutive interior)
• 2 angles between the
two lines on the same
side of transversal
Alternate Exterior Angles
• 2 angles outside the
two lines on opposite
sides of transversal
Determining what type of angle pair
1) Locate angles & determine which line is
transversal (this is always the line
containing one side of both angles)
2) On which side of the transversal are the
angles located?
1) Same side? Corresponding or SS Int (between
the two lines)
2) Opposite side?
1) Alternate interior (angles are between the two lines)
or
2) Alternate Exterior (angles are outside the two lines)
Determine relationship between the two angles.
5) <1 and <8
Alternate exterior
6) <1 and <14
Alternate exterior
7) <4 and <12
corresponding
1 2
5 6
9 10
13 14
4
3
78
12
11
15 16
Determine relationship between the two angles.
8) <6 and <10
Same-side interior
9) <11 and <16
Vertical Angles!!
10) <10 and <15
Alternate interior
1 2
5 6
4
3
78
10 11 12
9
13 14
15 16
Determine relationship between the two angles.
11) <1 and <2
Linear pair!
12) <6 and <9
Alternate interior
13) <8 and <12
Same side interior
1 2
5 6
4
3
78
9 10 11 12
13 14
15 16
Determine relationship between the two angles.
14) <2 and <5
Vertical Angles
15) <3 and <16
Alternate exterior
16) <8 and <16
corresponding
1 2
5 6
3 4
78
9 10 11 12
13 14
15 16
Determine relationship between the two angles.
17) <6 and <3
Alternate interior
18) <11 and <15
Linear pair
19) <5 and <7
corresponding
1 2
5 6
3 4
9 10 11
7 8
12
13 14 15 16
Name the transversal and the determine the relationships between the angles.
20) BCA and DGJ
p
q
B
Line p, alt ext
F
C
t
A
D
E
G
K
H
L
J
s
Name the transversal and the determine the relationships between the angles.
20) BCA and DGJ
p
q
B
Line p, alt ext
F
21) DGJ and FDE
C
t
Line q, corresponding
A
D
E
G
K
H
L
J
s
Name the transversal and the determine the relationships between the angles.
20) BCA and DGJ
p
q
B
Line p, alt ext
F
21) DGJ and FDE
Line q, corresponding
C
t
22) FDE and KHL
A
D
E
Line q, alt ext
G
K
H
L
J
s
Name the transversal and the determine the relationships between the angles.
20) BCA and DGJ
Line p, alt ext
21) DGJ and FDE
Line q, corresponding
22) FDE and KHL
Line q, alt ext
p
q
B
F
C
t
A
D
E
G
23) DGJ and GJH
Line p, alt int
K
H
L
J
s
Name the transversal and the determine the relationships between the angles.
20) BCA and DGJ
Line p, alt ext
21) DGJ and FDE
Line q, corresponding
22) FDE and KHL
Line q, alt ext
23) DGJ and GJH
Line p, alt int
p
q
B
F
C
t
A
D
E
G
24) CGH and GJH
Line p, corresponding
K
H
L
J
s
Name the transversal and the determine the relationships between the angles.
20) BCA and DGJ
Line p, alt ext
21) DGJ and FDE
Line q, corresponding
22) FDE and KHL
Line q, alt ext
23) DGJ and GJH
Line p, alt int
24) CGH and GJH
Line p, corresponding
p
q
B
F
C
t
A
D
E
G
25) BCA and CGH
Line p, corresponding
K
H
L
J
s