Download Properties of Parallel Lines

Aim: What are the properties of parallel lines?
Do Now: In each case, state why AB || CD :
1) B
A
85
D
95
C
B
2)
A
Int. 's, same side are suppl.
mA +mC  180
3)
A
C
4)
E
C
Alt. interior 's,
ABC  BCD
E
C
B
D
AB  BD and CD  BD
D
D
A
B
Corresp. 's
ECD  CAB
1
48l
3 7
m
2 6
Theorem #15:
1 5
k
Corresponding angles formed by a transversal and two parallel
lines are congruent. Ex: If m || k , then 1  3.
Theorem #16:
Alternate interior angles formed by a transversal and two
parallel lines are congruent. Ex: If m || k , then 3  6.
Theorem #17:
If parallel lines are cut by a transversal, then two interior
angles on the same side of the transversal are supplementary.
Ex: If m || k , m2  m3  180.
Theorem #18:
If a line is perpendicular to one of two parallel lines, it is
perpendicular to the other. Ex: If l  m and m || k , l  k .
Properties of parallel lines
Geometry Lesson: Properties of
Parallel Lines
2
Ex: Properties of Parallel Lines
If AB || CD, mBGH  3x  20 and mGHC  2 x  10 :
a) Determine x
b) Determine mCHF
a) BGH and GHC are alt. interior 's.
mBGH  mGHC
A
3x  20  2 x  10
x  30
C
b) mGHC  2(30)  10  70
mCHF  180  mGHC
mCHF  180  70
mCHF  110
Geometry Lesson: Properties of
Parallel Lines
E
G
B
D
H
F
3
Ex: Properties of Parallel Lines
A
Given FHD, FA || HB, mF  76
and mA  38, determine:
a) mBHD
b) mAHB
F
H
c) mAHD
B
D
a) F  BHD, (correpsonding angles)
mBHD  76
b) A  AHB, (alt. interior angles)
mAHB  38
c) mAHD  mAHB  mBHD
mAHD  38  76
Geometry Lesson: Properties of
Parallel Lines
4
Ex Proof w/parallel lines:
Given: RM  PQ , RM || PQ
Prove: RP || MQ
R
P
M
Q
Statements
Reasons
1) RM  PQ
2) RM || PQ
1) Given
2) Given
3) RMP  MPQ
3) Alt. int.  's formed by
4)
5)
6)
7)
transv. and || lines are  .
4) Reflexive Postulate
MP  MP
5) S.A.S. Postulate
RMP  QPM
RPM  QMP 6) C.P.C.T.C.
7) Lines cut by a transv. are ||
RP || MQ
Lesson: Properties of
ifGeometry
the alt.
int.
's are  .
Parallel Lines
5
Proofs w/parallel lines:
T
3) Given: FDQ, FT || DS
F
Prove: mTDQ  mTDN  mNDQ
N
D
S
2) Given: Isosceles QPD with QP  QD
QM || PD
Prove: D  SQM
Q
M
P
D
T
3) Given: MG || TD, MT || GD
Prove: G  T
M
Geometry Lesson: Properties of
Parallel Lines
Q
D
G
6
Ex w/parallel lines:
4) Lines l and k are parallel and
line m is a transversal. If m1  x  y ,
m2  2 x  y , and m3  2 y , find m1,
m2 and m3.
l
2
1 3
k
m
5) If AB || CD, AC || BD and m1=78,
determine m2, m3 and m4.
A
3
4
2
C
Geometry Lesson: Properties of
Parallel Lines
B
1
D
7