Name _______________________________________________________________ Date ___________________
Section 5-5 -- Practice A & B
Inequalities in One Triangle
Fill in the blanks to complete the theorems.
1. If two angles of a triangle are not congruent, then the longer side is
____________________ the larger angle.
2. The sum of any two side lengths of a triangle is ____________________
than the third side length.
3. If two sides of a triangle are not congruent, then the larger ____________________
is opposite the longer side.
4. Write the angles ofPQR in order from smallest to largest.
________________________________________
5. Write the sides ofGHI in order from shortest to longest.
________________________________________
Three segments have lengths of 5, 7, and 10. For Exercises 6–8 write
Yes or No. Write Yes for Exercise 9 only if the answer is yes for all of
Exercises 6–8.
6. Is 5  7  10? ________
7. Is 5  10  7? ________
8. Is 7  10  5? ________
9. Can the segments make a triangle?
____________________
10. Tell whether three segments with lengths 8, 15, and 6 can make a triangle.
________________________________________________________________________________________
For Exercises 11–15, a triangle has side lengths 11, 18, and n.
Solve Exercises 11–13 for n.
11. 11  18  n
________________________
12. 11  n  18
________________________
13. 18  n  11
________________________
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Holt McDougal Geometry
14. Exercises 12 and 13 tell what number n must be greater than.
Exercise 11 tells what number n must be less than. Complete
the inequality to find the values of n that will make a triangle
when used with the lengths 11 and 18.
________  n  ________
15. Tell whether the sides can make a triangle for each of these values of n:
a. n  3 _______________
b. n  21 _______________
c. n  35 _______________
16. Write the angles ofDEF in order from smallest to largest.
___________________________________________________
17. Write the sides ofGHI in order from shortest to longest.
___________________________________________________
Tell whether a triangle can have sides with the given lengths.
If not, explain why not.
18. 8, 8, 16 _______________ 19. 0.5, 0.7, 0.3 ________
1
20. 10 , 4, 14 ________
2
The lengths of two sides of a triangle are given. Find the range of
possible lengths for the third side.
21. 8.2 m, 3.5 m
________________________
22. 298 ft, 177 ft
________________________
23. 3
1
mi, 4 mi
2
________________________
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Holt McDougal Geometry
INDIRECT PROOF AND INEQUALITIES IN
ONE TRIANGLE
Practice A
1. opposite
2. greater
3. angle
4. Q; P; R
5. GI; GH; HI
6. yes
7. yes
8. yes
9. yes
10. The segments cannot make a triangle
because 8  6  15.
11. 29  n
12. n  7
13. n  7
15. a. no
14. 7; 29
b. yes
c. no
Practice B
1. m1  m2  m3  180°
2. Possible answer: Assume that m1 
m2  m3  180°. 4 is an exterior
angle of ABC, so by the Exterior
Angle Theorem, m1  m2  m4.
3 and 4 are a linear pair, so by the
Linear Pair Theorem, m3  m4 
180°. Substitution leads to the
conclusion that m1  m2  m3 
180°, which contradicts the assumption.
Thus the assumption is false, and the
sum of the angle measures of a triangle
cannot add to more than 180°.
3. F; D; E
5.no; 8  8  16
7. yes
4. HI;GH;GI
6. yes
8. yes
9. no; 12  20  36
10. 4.7 m  s  11.7 m
11. 121 ft  s  475 ft
12.
1
1
mi  s  7 mi
2
2
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry