Download Parallel Lines

Geometry
1
NAME: ______________________
Today we will revisit one of the most popular, however often misused theorems in Geometric Proofs.
Remember that parallel lines may NOT be congruent…
Parallel Lines
When given parallel lines, cut by a transversal you get:
Congruent Angles!
**Note: parallel lines are not automatically congruent**
Parallel lines cut by a transversal from congruent:
alternate interior angles
alternate exterior angles
corresponding angles
1. Prove the following relationships. (involving parallel lines)
P
a) GIVEN:
S
PT || SR &
TQ  SQ
PROVE:
PQT  RQS
STATEMENT
R
REASON
S
PT || SR &
PT  RS
Q
T
P
b) GIVEN:
PROVE:
PQT  RQS
STATEMENT
Q
T
R
REASON
2
c) GIVEN:
CB || ED & A is the
midpoint of CD
A
C
E
e) GIVEN:
B
REASON
l) GIVEN:
2
AB || CD & BC || DA
C
ABC  CDE
STATEMENT
REASON
3
A
A
PROVE:
B
EAD  BAC
STATEMENT
C
DE || CB , DG || CA &
D
4
D
REASON
PROVE:
EDG  BCA
STATEMENT
A
B
C
EG  BA
1
ABC  CDA
STATEMENT
AB || CD & BC || DE &
D
D
B
C is the midpoint of AE
PROVE:
PROVE:
d) GIVEN:
E
E
G
REASON