5
A drawing of a subway system shows the different levels used to reach the
subway platforms. Level 1 is line p, level 2 is line q, and level 3 is line r.
Prove that Level 2 and level 3 are parallel.
#H
PHOBB
Inbound trains
A
E
44°
Street
B
44°
m
Statements
1. m/ACB = 48°, mZCHI = 132°
2. mZDCH = 48°
48°
A
3. 48° +132° = 180°
4. mZDCH+mZCHI = 180°
5. ZDCH and ZCHI are supplementary.
6. p | q
7. MZEFY = 44°, mZFYZ = 44°
8. ZEFY LFYZ
9. pr
10. q- r
D
Reasons
1. Given
?
10.
Plaza
132
H
?
Outbound trains
2.
3.
Addition
4. Substitution Property of Equality
5. Definition of supplementary angles
?
A. What property justifies
mZDCH = 48°?
6.
7. Given
8. Definition of congruent angles
?
9.
B. What property justifies p || q?
C. What property justifies p || r?
D. What allows you to write q || r?