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


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

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!

c

a

b

Remember to visualize in 3D!

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


B

C

A

D

F

G

E

H

Parallel Planes: planes that will not intersect

Ex: Plane ABC and Plane FEH


N

M

E

H

T

X

O

R

S

G

A

1) Name all segments parallel to QX.

NE, MH, TO, SG, RA

Q


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


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


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

  • 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

  • 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)


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


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


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


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


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


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


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


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


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


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


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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