Geometry 3 1 relationships between lines
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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 and 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:. Ex: AB AE. B.

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Geometry 3.1: Relationships Between Lines

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Geometry 3 1 relationships between lines

Geometry 3.1: Relationships Between Lines


Geometry 3 1 relationships between lines

B

C

A

D

F

G

E

H

Parallel lines: Coplanar lines that never intersect and go in the same direction.

Symbols:

Ex: AB || DC


Geometry 3 1 relationships between lines

B

C

A

D

F

G

E

H

Perpendicular Lines: Intersect at a right angle.

Symbols:

Ex: AB AE


Geometry 3 1 relationships between lines

B

C

A

D

F

G

E

H

Skew Lines: noncoplanar lines that do not intersect and go in different directions

Ex: AB and DH


Careful

CAREFUL!

c

a

b

Remember to visualize in 3D!

Line c intersects line b, but lines a and c are skew.


Geometry 3 1 relationships between lines

B

C

A

D

F

G

E

H

Parallel Planes: planes that will not intersect

Ex: Plane ABC and Plane FEH


Geometry 3 1 relationships between lines

N

M

E

H

T

X

O

R

S

G

A

1) Name all segments parallel to QX.

NE, MH, TO, SG, RA

Q


Geometry 3 1 relationships between lines

N

M

E

H

T

X

O

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

Q


Geometry 3 1 relationships between lines

N

M

E

H

T

X

O

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

MT

HO

Q


Geometry 3 1 relationships between lines

N

M

E

H

T

X

O

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, MT, HO

Q

4) Name all segments skew to AG.

TO, MH, NE, XQ

TS, MT, NQ, QR


Transversal

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

Corresponding Angles

  • 2 angles in corresponding positions

    (same side of transversal, same respective side of lines)


Alternate interior angles

Alternate Interior Angles

  • 2 angles between the two lines on opposite sides of transversal


Same side interior angles aka consecutive interior

Same-Side Interior Angles(aka consecutive interior)

  • 2 angles between the two lines on the same side of transversal


Alternate exterior angles

Alternate Exterior Angles

  • 2 angles outside the two lines on opposite sides of transversal


Determining what type of angle pair

Determining what type of angle pair

  • Locate angles & determine which line is transversal (this is always the line containing one side of both angles)

  • On which side of the transversal are the angles located?

    • Same side? Corresponding or SS Int (between the two lines)

    • Opposite side?

      • Alternate interior (angles are between the two lines) or

      • 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

Determine relationship between the two angles.

4

1

2

3

5

8

6

7

12

11

9

10

16

13

14

15


Determine relationship between the two angles1

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.

4

1

2

3

5

8

6

7

11

12

10

9

16

13

14

15


Determine relationship between the two angles2

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.

2

4

1

3

5

8

6

7

11

12

9

10

16

13

14

15


Determine relationship between the two angles3

14) <2 and <5

Vertical Angles

15) <3 and <16

Alternate exterior

16) <8 and <16

corresponding

Determine relationship between the two angles.

2

4

1

3

5

8

6

7

11

12

9

10

16

13

14

15


Determine relationship between the two angles4

17) <6 and <3

Alternate interior

18) <11 and <15

Linear pair

19) <5 and <7

corresponding

Determine relationship between the two angles.

3

2

4

1

5

8

7

6

11

12

9

10

16

13

14

15


Geometry 3 1 relationships between lines

Name the transversal and the determine the relationships between the angles.

20) BCA and DGJ

Line p, alt ext

p

q

B

F

C

t

A

D

E

G

K

s

H

J

L


Geometry 3 1 relationships between lines

Name the transversal and the determine the relationships between the angles.

20) BCA and DGJ

Line p, alt ext

p

q

B

F

21) DGJ and FDE

Line q, corresponding

C

t

A

D

E

G

K

s

H

J

L


Geometry 3 1 relationships between lines

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

p

q

B

F

C

t

22) FDE and KHL

Line q, alt ext

A

D

E

G

K

s

H

J

L


Geometry 3 1 relationships between lines

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

s

H

J

L


Geometry 3 1 relationships between lines

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

s

H

J

L


Geometry 3 1 relationships between lines

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

s

H

J

L


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