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NAME ______________________________________________ DATE
5-2
____________ PERIOD _____
Skills Practice
Inequalities and Triangles
Determine which angle has the greatest measure.
3
1. ⬔1, ⬔3, ⬔4
2. ⬔4, ⬔5, ⬔7
3. ⬔2, ⬔3, ⬔6
4. ⬔5, ⬔6, ⬔8
1 2
5
4 6 7
Use the Exterior Angle Inequality Theorem to list all
angles that satisfy the stated condition.
8
2 4 7
5. all angles whose measures are less than m⬔1
1
3
5 6
8
9
Lesson 5-2
6. all angles whose measures are less than m⬔9
7. all angles whose measures are greater than m⬔5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8. all angles whose measures are greater than m⬔8
Determine the relationship between the measures of
the given angles.
9. m⬔ABD, m⬔BAD
23
A
10. m⬔ADB, m⬔BAD
B
34
35
C
41
39
D
11. m⬔BCD, m⬔CDB
12. m⬔CBD, m⬔CDB
Determine the relationship between the lengths of the
given sides.
13. L
苶M
苶, L
苶P
苶
M
83⬚ 57⬚
L
14. 苶
MP
苶, M
苶N
苶
38⬚
59⬚
79⬚ N
44⬚
P
15. 苶
MN
苶, N
苶P
苶
Chapter 5
16. 苶
MP
苶, L
苶P
苶
15
Glencoe Geometry
NAME ______________________________________________ DATE
5-2
____________ PERIOD _____
Word Problem Practice
Inequalities and Triangles
1. DISTANCE Carl and Rose live on the
same straight road. From their balconies
they can see a flagpole in the distance.
The angle that each person’s line of
sight to the flagpole makes with the
road is the same. How do their distances
from the flagpole compare?
4. SQUARES Matthew has three different
squares. He arranges the squares to
form a triangle as shown. Based on
the information, list the squares in
order from the one with the smallest
perimeter to the one with the largest
perimeter.
2. OBTUSE TRIANGLES Don notices that
the side opposite the right angle in a
right triangle is always the longest of
the three sides. Is this also true of the
side opposite the obtuse angle in an
obtuse triangle? Explain.
1
2
47˚
54˚
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. STRING Jake built a triangular
structure with three black sticks. He
tied one end of a string to vertex M
and the other end to a point on the
stick opposite M, pulling the string
taut. Prove that the length of the
string cannot exceed the longer of the
two sides of the structure.
CITIES For Exercises 5 and
Dallas
6, use the following
64˚
information.
59˚
Stella is going to
Abilene
Texas to visit a friend.
As she was looking at a
Austin
map to see where she
might want to go, she noticed
the cities Austin, Dallas, and Abilene
formed a triangle. She wanted to determine
how the distances between the cities were
related, so she used a protractor to measure
two angles.
M
string
5. Based on the information in the figure,
which of the two cities are nearest to
each other?
6. Based on the information in the figure,
which of the two cities are farthest apart
from each other?
Chapter 5
17
Glencoe Geometry
Lesson 5-2
3