 # 5-7 Practice Inequalities in Two Triangles

```Name
Class
Date
Practice
5-7
Form K
Inequalities in Two Triangles
Write an inequality relating the given side lengths. If there is not enough
information to reach a conclusion, write no conclusion.
1. AB and CB AB R CB
A
To start, determine whether the triangles have two pairs of
congruent sides.
B
D
100
C
DB > 9 DB
Then compare the hinge angles.
u
80
m/ z ADB z 5 u
m/CDB 5 100
2. JL and MO JL S MO
3. ST and BT no conclusion
N
K
60
S
B
44
J
M
T
30
35
C
O
L
4. Two identical laptops are shown at the right.
Top edge
In which laptop is the distance from the top edge of
the screen to the front edge of the keyboard greater?
Explain.
45
Laptop B; the lengths of the laptops’ keyboards and
screens are the same. Laptop B is open wider, so the
hinge angle is greater than it is for Laptop A.
A
Front edge
Algebra Find the range of possible values for each variable.
5.
(3x 15) D
6.
48
66
(2x 4)
28
C
23 F
u
x , 27
50
25 E
m/CDF , m/EDF
m/CDE . 0
x.
16
2 ,x, u
u
5
u
Prentice Hall Foundations Geometry • Teaching Resources
65
70
B
Name
Class
Date
Practice (continued)
5-7
Form K
Inequalities in Two Triangles
Use the diagram at the right for Exercises 7–9.
Complete each comparison with R or S. Then
complete the explanation.
A
D
C
46 90
u
7. m/ACB S m/DCE
45
B
45
z lDCE z forms a straight angle with z lBCE z and z lACB z.
u
The measure of /DCE is 44 .
u
8. AB S DE
u u
Because nBCE is an isosceles triangle, BC 5 CE .
z kACB z and z kDCE z have two pairs of congruent sides.
u
So, by the 9 Theorem, AB S DE.
u
Hinge
9. BE S CE
The longest side of a n is opposite the angle with the 9 measure.
greatest
10. The diagram shows two paths that lead through a park.
Would a jogger run a greater distance on Path A or Path B?
Explain.
Path A; the paths have two pairs of congruent sides, but
Path A angles off at 268, while Path B angles off at 258.
The longer side is the one opposite the greater angle.
i
B
Path
25
26
Pat
hA
12. m/U and m/X mlU R mlX
11. m/M and m/R mlM S mlR
M
N
U
4
V
O
7
P
10.5
9
4
8
2m
i
Write an inequality relating the given angle measures.
4
2m
11
W
X
Q
9
4
Y
R
10.5
12
Z
MN , MO, PR, and QR are 9. congruent
u
NO S PQ
Prentice Hall Foundations Geometry • Teaching Resources  