Preparing for the Regents Examination Geometry, AK

28 mBDA mACB because a whole is
greater than its parts. mACB mBCA
because they are opposite congruent sides
of a triangle. So mBDA mBCA by the
substitution postulate of inequality, and
AB AD because the greater side lies
opposite the greater angle.
29 Draw diagonal −−
AC , forming two triangles.
In ABC, mBCA mBAC because
they are opposite congruent sides. In
ADC, mACD mCAD because the
greater angle is opposite the greater side.
mBCA mACD mBAC mCAD
or mBCD mBAD by the addition postulate
of inequality.
30 Look at the two right triangles formed with
common side −−
EG . mD mF by the subtraction
postulate of inequality, so DE EF
because the greater side lies opposite the
greater angle.
CHAPTER
8
8-1 The Slope of a Line
(pages 141–144)
1 (2) (0, 4)
2 (2) It has an x-intercept of 2.
3 (4) y 3
4 (3) a y-intercept of 5
5 (3)
6 (2) x 1
7 m 5 _ ; negative
3
8 m 2; positive
9 m 3 _ ; positive
4
31 m2 180 114 66
m1 180 50 66 64
32 x 4 5 105
x 60
33 y 18 0 110 70
x 7 0 130
x 60
34 True
35 False
36 True
37 False
38 False
Slopes and Equations
of Lines
10 Undefined
11 m 2; negative
12 m 3 _ ; positive
2
13 m 0; zero
14 m 1 _ ; positive
2
15 m 3; positive
16 a y 5
b y 1
c x 2
d x 10
e y 4.5
8-1 The Slope of a Line 39