Congruence
PRE-ALGEBRA LESSON 9-5
(For help, go to Lesson 6-3.)
ABC ~ XYZ. For the given part of
part of XYZ.
1.
A
3. AB
2.
ABC, find the corresponding
C
4. CA
Check Skills You’ll Need
9-5
Congruence
PRE-ALGEBRA LESSON 9-5
Solutions
1.
X
3. XY
2.
Z
4. ZX
9-5
Congruence
PRE-ALGEBRA LESSON 9-5
In the figure,
TUV
WUX.
a. Name the corresponding congruent angles.
X, T
W , TUV
WUX
V
b. Name the corresponding congruent sides.
TV
WX , TU
WU , VU
XU
c. Find the length of WX.
Since WX,
TV, and TV = 300 m, WX = 300 m.
9-5
Quick Check
Congruence
PRE-ALGEBRA LESSON 9-5
List the congruent corresponding parts of each pair of
triangles. Write a congruence statement for the triangles.
a.
ACB
AC
ECD
EC
Angle
Side
CAB
CED
ACB
ECD by ASA.
9-5
Angle
Congruence
PRE-ALGEBRA LESSON 9-5
(continued)
b.
MK
MKJ
JK
MKJ
LJ
LJK
JK
Side
Angle
Side
LJK by SAS.
Quick Check
9-5
Congruence
PRE-ALGEBRA LESSON 9-5
Given that
1.
L
O
JKL
MNO, complete the following.
2. JK
MN
3. JL
MO
4. If two sides and the angle between those sides of one triangle
are congruent to two sides and the angle between those sides
of another triangle, why can you conclude that the two triangles
are congruent?
SAS
9-5
Circles
PRE-ALGEBRA LESSON 9-6
Solve the proportion:
4
n
=
5
27
n = 21 3
5
9-6
Circles
PRE-ALGEBRA LESSON 9-6
(For help, go to Lesson 6-2.)
Solve each proportion. Round to the nearest whole number where
necessary.
1.
10
x
=
100
360
2.
75
x
=
100
360
3.
0.8
x
=
5.3
360
4.
1.6
x
=
5.3
360
Check Skills You’ll Need
9-6
Circles
PRE-ALGEBRA LESSON 9-6
Solutions
1. 36
2. 270
3. 54
4. 109
9-6
Circles
PRE-ALGEBRA LESSON 9-6
Find the circumference of the circle.
C=
C
d
Write the formula.
(3.14)(2)6
Replace
= 37.68
with 3.14 and d with (2)6.
Simplify.
The circumference of the circle is about 37.68 in.
Quick Check
9-6
Circles
PRE-ALGEBRA LESSON 9-6
Make a circle graph for Jackie’s weekly budget.
Jackie’s Weekly Budget
Entertainment (e)
20%
Food (f)
20%
Transportation (t)
10%
Savings (s)
50%
Use proportions to find the measures
of the central angles.
20
e
=
100
360
20
f
=
100
360
e = 72°
f = 72°
10
t
=
100
360
50
s
=
100
360
t = 36°
9-6
s = 180°
Circles
PRE-ALGEBRA LESSON 9-6
(continued)
Use a compass to draw a circle.
Draw the central angles with a protractor.
Label each section.
Add a title.
Jackie’s Weekly Budget
Entertainment
Savings
Food
Transportation
9-6
Quick Check
Circles
PRE-ALGEBRA LESSON 9-6
Draw a circle graph of the data.
First add to find the total number of students.
Spring Dance Attendance
Freshmen (f)
Sophomores (p)
120
82
Juniors (j)
137
Seniors (s)
101
120 + 82 + 137 + 101 = 440
Use proportions to find the measures
of the central angles.
120
f
=
440
360
f
98°
137
j
=
440
360
j
9-6
112°
82
p
=
440
360
p
67°
101
s
=
440
360
s
83°
Circles
PRE-ALGEBRA LESSON 9-6
(continued)
Use a compass to draw a circle.
Draw the central angles with a protractor.
Label each section.
Add a title.
Spring Dance Attendance
Seniors
Juniors
Freshmen
Sophomores
Quick Check
9-6
Circles
PRE-ALGEBRA LESSON 9-6
Solve.
1. Find the circumference of a circle with a diameter of 2.5 in.
about 7.85 in.
2. Ten out of 22 students surveyed prefer milk with their breakfast.
Find the measure of the central angle to represent this data in a
circle graph.
about 164°
3. Draw a circle graph of the data.
After-School Number of
Activities
(for one class)
Band
Basketball
Baby-sitting
Library
9-6
Students
5
8
10
7