Download HW Practice B Section 2-2

Name ________________________________________ Date __________________ Class__________________
Practice B
LESSON
2-2
Algebraic Proof
Solve each equation. Show all your steps and write a justification for each step.
1.
1
(a 10)
5
3
2. t 6.5
3t 1.3
3. The formula for the perimeter P of a rectangle with length A and width w is
P 2(A w). Find the length of the rectangle shown here if the perimeter is 9
1
feet.
2
Solve the equation for A and justify each step.
Write a justification for each step.
4.
HI IJ
HJ
___________________
7x 3
(2x 6) (3x 3)
___________________
7x 3
5x 3
___________________
7x
5x 6
___________________
2x
6
___________________
x
3
___________________
Identify the property that justifies each statement.
5. m
n, so n
6. ‘ABC # ‘ABC
m.
_________________________________________
________________________________________
7. KL # LK
8. p
_________________________________________
q and q
1, so p
1.
________________________________________
‹+RXJKWRQ0LIIOLQ+DUFRXUW3XEOLVKLQJ&RPSDQ\
50
Holt McDougal Analytic Geometry
2. No; time is also a factor in freeride races,
so the converse is false.
13. 8; 20.32; c; 20.32
14. Seg. Add. Post.; Subst.; Simplify.; Subtr.
Prop. of ; Mult. Prop. of
3. Yes; a mountain bike race covers 250
kilometers if and only if it is a marathon
race.
Practice B
1.
ª1
º
5 « a 10 » 5 3 5
¬
¼
4. No; a downhill race does not contain
cliffs, drops, and ramps, so the converse
is false.
5. C
6. G
a 10
a 10 10
Reading Strategies
a
1. Biconditional statement: PossibleJJJJ
answer:
G
m‘WXY m‘YXZ if and only if XY is
the angle bisector.
Conditional: Answers will vary. Sample
JJJJG
answer: If m‘WXY m‘YXZ, then XY
is the angle bisector.
JJJJG
Converse: Possible answer: If XY is the
angle bisector, then m‘WXY m‘YXZ.
Definition of an angle bisector: Possible
answer: An angle bisector divides an
angle into two angles of equal measure.
2.
t 6.5 t
6.5
15
(Mult. Prop. of )
(Simplify.)
15 10 (Subtr. Prop. of )
–25
(Simplify.)
3t 1.3 t
(Subtr. Prop. of )
2t 1.3
(Simplify.)
6.5 1.3 2t 1.3 + 1.3
(Add. Prop. of )
7.8
2t
(Simplify.)
7.8
2
2t
2
(Div. Prop. of )
3.9
t
(Simplify.)
3.9
(Symmetric Prop. of )
t
3.
2. Biconditional statement: Possible answer:
‘FGH and ‘QRS are complementary
angles if and only if m‘FGH m‘QRS
90°.
Conditional: Possible answer: If ‘FGH
and ‘QRS are complementary angles,
then m‘FGH m‘QRS 90°.
Converse: Possible answer: If m‘FGH m‘QRS 90°, then they are
complementary angles.
Definition of complementary angles:
Possible answer: Two angles whose
measures sum to 90° are complementary
angles.
2(A w)
P
(Given)
1
1·
§
2 ¨ A 1 ¸
(Subst. Prop. of )
2
4¹
©
1
1
2A 2
(Distrib. Prop.)
9
2
2
1
1
1
1
2A 2 2 (Subtr. Prop. of )
9 2
2
2
2
2
9
7
2A
(Simplify.)
7
2A
2
(Div. Prop. of )
3
2-2 ALGEBRAIC PROOF
A
1
2
A
3
1
2
(Simplify.)
(Symmetric
Prop. of )
Practice A
1. F
2. C
3. J
4. E
5. A
6. I
7. G
8. K
9. L
10. D
11. H
12. B
© Houghton Mifflin Harcourt Publishing Company
A8
Holt McDougal Analytic Geometry
4. Possible answer: The Substitution
Property states that if a b, then b can
be substituted for a in any expression.
Applying the Symmetric Property to the
Substitution Property shows that if b a,
then a can be substituted for b in any
expression. So if a b and b c, then
a c by the Substitution Property, and
this is also the Transitive Property.
4.
Seg. Add. Post.
Subst. Prop. of
Simplify.
Add. Prop. of
Subtr. Prop. of
Div. Prop. of
5. Symmetric Prop. of
5. Possible answer: Consider the points
A(0, 1), B(1, 0), C(0, 1), and D(1, 0).
For reflection across the x-axis, the
image of AB is CB. AB # AD , but you
cannot conclude that the image of AD is
CB for reflection across the x-axis.
Reteach
6. Reflexive Prop. of #
7. Reflexive Prop. of #
8. Transitive Prop. of
or Subst.
Practice C
1.
m‘1 m‘2
90°
(Given)
m‘2 m‘3
180°
(Given)
1.
3
m‘2 m‘3 (m‘1 m‘2)
180° 90°
(Subtr. Prop. of )
m‘3 m‘1
m‘3
90°
m‘1 90°
(Simplify.)
(Given)
‘ZYX # ‘XYZ
(Reflexive Prop. of #)
‘ZYX # ‘ABC
(Trans. Prop. of #)
m‘ABC
‘ABD # ‘CBD
m‘ABD
m‘CBD
n
(6)
6
(Add. Prop. of )
2.
‘XYZ # ‘ABC
m‘ZYX
n
6
n
x
(Def. of ‘ bisector)
m‘ABC m‘CBD
m‘CBD
(Subst. Prop. of )
m‘ABC
2m‘CBD
(Simplify.)
m‘ZYX
2m‘CBD
(Subst. Prop. of )
13
Simplify.
13(6)
Mult. Prop. of
78
Simplify.
x Subtr. Prop. of
5
x
Simplify.
x
5
Sym. Prop. of
3.
(Def. of #)
(‘ Add. Post.)
Add. Prop. of
2.
(Def. of #)
m‘ABC m‘ABD
m‘CBD
3
y 4
(7)
7
3(7)
Mult. Prop. of
y4
21
Simplify.
4
4
Subtr. Prop. of
y
17
Simplify.
4.
4t 12 20
12 12
4t 8
4t 8
4 4
t 2
3. (x y) a; a(c d) ac ad; ac ad
c(x y) d(x y); c(x y) d(x y) cx
cy dx dy; (x y)(c d) cx cy dx dy
Distr. Prop.
Add Prop. of
Simplify.
Div. Prop. of
Simplify.
© Houghton Mifflin Harcourt Publishing Company
A9
Holt McDougal Analytic Geometry