geometry 3.1: relationships between lines

Geometry 3.1: Relationships Between Lines

Parallel lines: Coplanar lines that never intersect and 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 and 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 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