Preparing for the Regents Examination Geometry, AK

___ 27 a M KA (5, 1), M ___
AT (4, 3), M ___
TK (2, 1)
___ b m KA 1, m ___
AT 0, m ___
TK 2
c Slope of line perpendicular to ___
KA is 1.
There is no slope for the line perpendicular
to ___
AT . Slope of the line perpendicular
to ___
TK is 1 _ .
2
d Perpendicular bisector of ___
KA : y x 6
Perpendicular bisector of ___
AT : x 4
Perpendicular bisector of ___
TK : y 1 _ x
2
e (4, 2)
Parallel Lines
9-2 Proving Lines Parallel
(pages 177–179)
1 none
2 a b, c d
3 none
4 b c
5 a b
6 a c
7 b c
8 l m
9 a and b
10 c and d
11 a and b
Note: Since there are many variations of proofs,
the following is simply one set of acceptable
statements to complete each proof. Depending
on the textbook used, the wording and format
of reasons may differ, so they have not been
supplied for the method of congruence applied
in each problem. (These solutions are intended
to be used as a guide—other possible solutions
may vary.)
44 Chapter 9: Parallel Lines
28 a y 2x 5
b (6, 8)
c y 1 _ x 5
2
CHAPTER
9
12 1. 1 3
2. 2 4
3. 1 2 3 4 (Addition postulate
of equality)
4. ABG DEG
5. −−
ED −−
BA (If two lines are cut by a transversal
forming a pair of congruent
alternate interior angles,
the two lines are parallel.)
13 1. ___
AF ___
CD
2. −−
FC ___
FC
3. −−
AF −−
FC ___
CD ___
FC
4. ___
AC ___
DF
5. −−
BC ___
EF
6. ___
BC ___
AD
7. BCF is a right angle. (Definition of
right angle)
8. ___
EF ___
AD
9. EFD is a right angle.
10. BCF EFD (Right angles are
congruent)
11. ABC DEF (SAS SAS)