Preparing for the Regents Examination Geometry, AK

6. 2 and 1 are supplementary.
7. (b) 5 1 (Supplements of the same
angle are congruent.)
19 a (x 12) (3x) 180
x 42
m1 m3 m5 54
m2 m4 m6 126
b (2x) (2x 20) 180
x 50
m1 m3 m5 100
m2 m4 m6 80
c (7x 65) (5x 5)
x 30
m2 m5 145
m1 m3 m4 m6 35
20 a 5
b 7
c 6 and 8
d m5 60
e m4 90
21 Since the corresponding angles are congruent,
the halves of each are congruent. They
form new congruent corresponding angles
cut by the same transversal. The bisectors are
therefore parallel.
22 Draw a diagonal line, forming two congruent
triangles by SAS. The other two sides of
the quadrilateral and remaining angles are
congruent by CPCTC. Therefore, since the
diagonal is a transversal for these sides, the
sides are parallel.
9-4 Parallel Lines in the
Coordinate Plane
(pages 187–188)
1 a 4
b 7 _
3
c 2 _
5
d x _
a
2 a 1
b 3 _
5
c 2 _
5
3 a 1 _
4
b 7
c 1
d 3 _
2
4 a perpendicular
b parallel
c perpendicular
d parallel
e perpendicular
f neither
5 a 1
b 5 _
2
c 3 _
10
d 7 _
9
e 4 _
3
f 3 _
2
6 a 7
b 1
c 11
d no slope
e 0
f 1 _
2
___
7 a Slope AB 7, slope ___
1
CD _ ,
7 ___
AB ___
CD
___ b Slope AB 2, slope ___
1
CD _ ,
2 ___
AB ___
CD
8 y 5x 3
9 y = 1 _ x 3
5
10 y 3 _ x
2 7 _
2
11 y 1 _ x 3
3
12 y 4
13 y 2x 6
14 y 2 _ x 9
3
15 k = 1
16 (7, 5)
___ 17 Slope
4
AB _
3
___ , slope CD
3 _ . The slopes are
4
negative reciprocals, therefore −−
AB and −−−
CD
are perpendicular and ABC is a right
triangle.
18 Opposite sides have the same slope.
___ m PQ m ___
1
RS _
___ and m PS 3 m ___ 5 QR
19 H(5, 6)
20 a D(4, 3)
9-4 Parallel Lines in the Coordinate Plane 47