Complete each statement. Justify your answer.
- If
4
m
=
9
n
,
4 m equals 9 n comma then
m
n
=
□
□
.
m over n , equals , fraction white square , over white square end fraction , .
- If
30
t
=
18
r
,
30 over t , equals , 18 over r , comma then
t
r
=
□
□
.
t over r , equals , fraction white square , over white square end fraction , .
- If
a
+
5
5
=
b
+
2
2
,
fraction eh plus 5 , over 5 end fraction . equals . fraction b plus 2 , over 2 end fraction . comma then
a
5
=
□
□
.
eh over 5 , equals , fraction white square , over white square end fraction , .
- If
a
b
=
c
d
,
eh over b , equals , c over d , comma then
a
+
b
c
+
d
=
□
□
.
fraction eh plus b , over c plus d end fraction . equals , fraction white square , over white square end fraction , .
- If
a
b
=
c
d
,
eh over b , equals , c over d , comma then
a
+
c
b
+
d
=
□
□
.
fraction eh plus c , over b plus d end fraction . equals , fraction white square , over white square end fraction , .
- If
a
b
=
c
d
,
eh over b , equals , c over d , comma then
a
+
2
b
b
=
□
□
.
fraction eh plus 2 b , over b end fraction . equals , fraction white square , over white square end fraction , .
C Challenge
Algebra Use properties of equality to justify each property of proportions.
-
a
b
=
c
d
eh over b , equals , c over d is equivalent to
b
a
=
d
c
.
b over eh , equals , d over c , .
-
a
b
=
c
d
eh over b , equals , c over d is equivalent to
a
c
=
b
d
.
eh over c , equals , b over d , .
-
a
b
=
c
d
eh over b , equals , c over d is equivalent to
a
+
b
b
=
c
+
d
d
.
fraction eh plus b , over b end fraction . equals . fraction c plus d , over d end fraction . .
Algebra Solve each proportion for the variable(s).
-
x
−
3
3
=
2
x
+
2
fraction x minus 3 , over 3 end fraction . equals . fraction 2 , over x plus 2 end fraction
-
3
−
4
x
1
+
5
x
=
1
2
+
3
x
fraction 3 minus 4 x , over 1 plus 5 x end fraction . equals . fraction 1 , over 2 plus 3 x end fraction
-
x
6
=
x
+
10
18
=
4
x
y
x over 6 , equals . fraction x plus 10 , over 18 end fraction . equals , fraction 4 x , over y end fraction
Standardized Test Prep
SAT/ACT
GRIDDED RESPONSE
- In the diagram below,
B
D
¯
b d bar is the perpendicular bisector of
A
C
¯
.
eh c bar , . What is the length of
E
A
¯
?
e eh bar , question mark
- The measures of the angles of a triangle are in the extended ratio 6 : 3 : 1. What is the measure of the largest angle?
-
In the diagram below,
△
A
B
C
white up pointing triangle eh b c is an isosceles triangle with base
A
C
¯
eh c bar and
m
∠
A
B
C
=
40
.
m angle eh b c , equals 40 , . What is the value of x?
- In
△
P
Q
R
,
P
Q
=
10
in
.
white up pointing triangle p q r comma p q , equals 10 , in , . and
Q
R
=
12
in
.
q r , equals 12 , in , . RP must be less than x inches. What is the value of x?
- What is the length of the line segment joining
P
(
−
3
,
−
2
)
p open minus , 3 comma negative 2 close and Q(9, 3)?
Mixed Review
See Lesson 6-9.
66. Write a coordinate proof of this statement: The diagonals of a square are perpendicular.
See Lessons 1-5 and 5-5.
In each exercise, identify two statements that contradict each other.
-
-
△
P
Q
R
white up pointing triangle p q r is isosceles.
-
△
P
Q
R
white up pointing triangle p q r is an obtuse triangle.
-
△
P
Q
R
white up pointing triangle p q r is scalene.
-
-
∠
1
≅
∠
2
angle , 1 approximately equal to , angle 2
-
∠
1
angle 1 and
∠
2
angle 2 are complementary.
-
m
∠
1
+
m
∠
2
=
180
m angle , 1 plus , m angle , 2 equals 180
Get Ready! To prepare for Lesson 7-2, do Exercise 69.
See Lesson 4-1.
-
△
A
B
C
≅
△
H
I
J
.
white up pointing triangle eh b c approximately equal to white up pointing triangle h i j . Name three pairs of congruent angles and three pairs of congruent sides.
