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Geometry 3.1: Relationships Between Lines. B. C. A. D. F. G. E. H. Parallel lines: Coplanar lines that never intersect (they will go in the same direction). Symbols:. Ex: AB || DC. B. C. A. D. F. G. E. H. Perpendicular Lines: Intersect at a right angle. Symbols:. - PowerPoint PPT Presentation
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Geometry 3.1: Relationships Between Lines
Parallel lines: Coplanar lines that never intersect (they will go in the same direction).
Symbols:
Ex: AB || DC
A
H
GF
E
D
CB
Perpendicular Lines: Intersect at a right angle.
Symbols:
Ex: AB AEA
H
GF
E
D
CB
Skew Lines: Noncoplanar lines that do not intersect (they will go in different directions)
Ex: AB and DH
A
H
GF
E
D
CB
CAREFUL!
a
b
c
Remember to visualize in 3D!
Line c intersects line b, but lines a and c are skew.
A
H
GF
E
D
CB
Parallel Planes: planes in the same direction that will not intersect
Ex: Plane ABC and Plane FEH
S
O
T
H
M N
E
X
AG
R
Q
1) Name all segments parallel to QX.
NE, MH, TO, SG, RA
S
O
T
H
M N
E
X
AG
R
Q
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
S
O
T
H
M N
E
X
AG
R
Q
1) Name all segments parallel to QX.NE, MH, TO, SG, RA
2) Name all planes that intersect plane MHE.Planes MNQMHTHEXNEX
3) Name all segments parallel to QR.
XA
MT
HO
S
O
T
H
M N
E
X
AG
R
Q
1) Name all segments parallel to QX.NE, MH, TO, SG, RA
2) Name all planes that intersect plane MHE.Planes MNQMHTHEXNEX
3) Name all segments parallel to QR.
XA, MT, HO4) Name all segments skew to AG.
TO, MH, NE, XQ
TS, MT, NQ, QR
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 pair1) 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.
8
4321
765
121110913 14 15 16
5) <1 and <8
Alternate exterior
6) <1 and <14
Alternate exterior
7) <4 and <12
corresponding
Determine relationship between the two angles.
8
4321
765
121110913 14 15 16
8) <6 and <10
Same-side interior
9) <11 and <16
Vertical Angles!!
10) <10 and <15
Alternate interior
Determine relationship between the two angles.
8
4321
765
1211109
13 14 15 16
11) <1 and <2
Linear pair!
12) <6 and <9
Alternate interior
13) <8 and <12
Same side interior
Determine relationship between the two angles.
8
4321
765
1211109
13 14 15 16
14) <2 and <5
Vertical Angles
15) <3 and <16
Alternate exterior
16) <8 and <16
corresponding
Determine relationship between the two angles.
8
4321
765
1211109
13 14 15 16
17) <6 and <3
Alternate interior
18) <11 and <15
Linear pair
19) <5 and <7
corresponding
Name the transversal and the determine the relationships between the angles.
G
ED
F
C
B
A
p
t
L
KJH
q
s
20) BCA and DGJ
Line p, alt ext
Name the transversal and the determine the relationships between the angles.
G
ED
F
C
B
A
p
t
L
KJH
q
s
21) DGJ and FDE
Line q, corresponding
20) BCA and DGJ
Line p, alt ext
Name the transversal and the determine the relationships between the angles.
G
ED
F
C
B
A
p
t
L
KJH
q
s
22) FDE and KHL
Line q, alt ext
20) BCA and DGJ
Line p, alt ext21) DGJ and FDELine q, corresponding
Name the transversal and the determine the relationships between the angles.
G
ED
F
C
B
A
p
t
L
KJH
q
s
23) DGJ and GJH
Line p, alt int
20) BCA and DGJ
Line p, alt ext21) DGJ and FDELine q, corresponding22) FDE and KHLLine q, alt ext
Name the transversal and the determine the relationships between the angles.
G
ED
F
C
B
A
p
t
L
KJH
q
s
24) CGH and GJH
Line p, corresponding
20) BCA and DGJ
Line p, alt ext21) DGJ and FDELine q, corresponding22) FDE and KHLLine q, alt ext23) DGJ and GJHLine p, alt int
Name the transversal and the determine the relationships between the angles.
G
ED
F
C
B
A
p
t
L
KJH
q
s
25) BCA and CGH
Line p, corresponding
20) BCA and DGJ
Line p, alt ext21) DGJ and FDELine q, corresponding22) FDE and KHLLine q, alt ext23) DGJ and GJHLine p, alt int24) CGH and GJHLine p, corresponding
