Answer:
Explanation:
1. 5 cm, 7 cm, 10 cm
SOLUTION:
The sum of the lengths of any two sides of a triangle
must be greater than the length of the third side.
5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5
Thus, you can form a triangle with side lengths 5 cm,
7 cm, and 10 cm.
ANSWER:
Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5
2. 3 in., 4 in., 8 in.
ANSWER:
No;
3. 6 m, 14 m, 10 m
ANSWER:
Yes; 6 + 14 > 10, 6 + 10 > 14, and 10 + 14 > 6
4. MULTIPLE CHOICE If the measures of two
sides of a triangle are 5 yards and 9 yards, what is
the least possible measure of the third side if the
measure is an integer?
A 4 yd
B 5 yd
C 6 yd
D 14 yd
The correct option is B.
ANSWER:
B
PROOF Write a two-column proof.
5. Given:
Given:
Prove: YZ + ZW > XW
Proof:
Statements (Reasons)
1. (Given)
2. XW = YW (Def. of segments)
3. YZ + ZW > YW ( Inequal. Thm.)
4. YZ + ZW > XW (Substitution Property.)
ANSWER:
Given:
Prove: YZ + ZW > XW
Proof:
Statements (Reasons)
1. (Given)
2. XW = YW (Def. of segments)
3. YZ + ZW > YW ( Inequal. Thm.)
4. YZ + ZW > XW (Subst.)
Is it possible to form a triangle with the given
side lengths? If not, explain why not.
6. 4 ft, 9 ft, 15 ft
ANSWER:
No;
7. 11 mm, 21 mm, 16 mm
ANSWER:
Yes; 11 + 21 > 16, 11 + 16 > 21, and 16 + 21 > 11
8. 9.9 cm, 1.1 cm, 8.2 cm
No;
9. 2.1 in., 4.2 in., 7.9 in.
ANSWER:
No;
10.
No;
11.
ANSWER:
Yes;
Find the range for the measure of the third side
of a triangle given the measures of two sides.
12. 4 ft, 8 ft
ANSWER:
4 ft < n < 12 ft
13. 5 m, 11 m
ANSWER:
6 m < n < 16 m
14. 2.7 cm, 4.2 cm
ANSWER:
1.5 cm < n < 6.9 cm
15. 3.8 in., 9.2 in.
13.
ANSWER:
5.4 in. < n < 13 in.
16.
ANSWER:
17.
ANSWER:
Proof:
Statements (Reasons)
1. (Given)
2. (Conv. Isos. Thm.)
3. BC = BD (Def. of segments)
4. AB + AD > BD ( Inequal. Thm.)
5. AB + AD > BC (Subst.)
19. Given:
Prove: KJ +KL> LM
Proof:
Statements (Reasons)
1. (Given)
2. JL = LM (Def. of segments)
3. KJ + KL > JL ( Inequality Thm.)
4. KJ + KL > LM (Substitution Property)
ANSWER:
Proof:
Statements (Reasons)
1. (Given)
2. JL = LM (Def. of segments)
3. KJ + KL > JL ( Inequal. Thm.)
4. KJ + KL > LM (Subst.)
SENSE-MAKING Determine the possible
values of x.
20.
Notice that is always true for any whole
number measure for x.The range of values that
would be true for the other two inequalities is
and , which can be written as
.
ANSWER:
6 < x < 17
21.
ANSWER:
22. TRAVEL Keyan wants to take the most efficient
route from his hotel to the hockey game at The
Sportsplex. He can either take Highway 521 or
take Highway 3 and Route 11 from his hotel to the
arena.
a. Which of these two possible routes is the shorter?
Explain your reasoning.
b. Suppose Keyan always drives the speed l
Is it possible to form a triangle with the given
side lengths? If not, explain why not.
1. 5 cm, 7 cm, 10 cm
ANSWER:
Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5
2. 3 in., 4 in., 8 in.
ANSWER:
No;
3. 6 m, 14 m, 10 m
ANSWER:
Yes; 6 + 14 > 10, 6 + 10 > 14, and 10 + 14 > 6
4. MULTIPLE CHOICE If the measures of two
sides of a triangle are 5 yards and 9 yards, what is
the least possible measure of the third side if the
measure is an integer?
A 4 yd
B 5 yd
C 6 yd
D 14 yd
ANSWER:
B
Given:
Prove: YZ + ZW > XW
Proof:
Statements (Reasons)
1. (Given)
2. XW = YW (Def. of segments)
3. YZ + ZW > YW ( Inequal. Thm.)
4. YZ + ZW > XW (Subst.)
Is it possible to form a triangle with the given
side lengths? If not, explain why not.
6. 4 ft, 9 ft, 15 ft
ANSWER:
No;
7. 11 mm, 21 mm, 16 mm
SOLUTION:
ANSWER:
Yes; 11 + 21 > 16, 11 + 16 > 21, and 16 + 21 > 11
8. 9.9 cm, 1.1 cm, 8.2 cm
SOLUTION:
T
No;
9. 2.1 in., 4.2 in., 7.9 in.
No;
10.
ANSWER:
No;
11.
.
ANSWER:
Yes;
Find the range for the measure of the third side
of a triangle given the measures of two sides.
12. 4 ft, 8 ft
4 ft < n < 12 ft
13. 5 m, 11 m
6 m < n < 16 m
14. 2.7 cm, 4.2 cm
ANSWER:
1.5 cm < n < 6.9 cm
15. 3.8 in., 9.2 in.
13.
ANSWER:
5.4 in. < n < 13 in.
16.
Proof:
Statements (Reasons)
1. (Given)
2. JL = LM (Def. of segments)
3. KJ + KL > JL ( Inequal. Thm.)
4. KJ + KL > LM (Subst.)
SENSE-MAKING Determine the possible
values of x.
20.
SOLUTION:
Set up and solve each of the three triangle
inequalities.
ANSWER:
6 < x < 17
21.
ANSWER:
Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5
2. 3 in., 4 in., 8 in.
ANSWER:
No;
3. 6 m, 14 m, 10 m
ANSWER:
Yes; 6 + 14 > 10, 6 + 10 > 14, and 10 + 14 > 6
4. MULTIPLE CHOICE If the measures of two
sides of a triangle are 5 yards and 9 yards, what is
the least possible measure of the third side if the
measure is an integer?
A 4 yd
B 5 yd
C 6 yd
D 14 yd
The correct option is B.
ANSWER:
B
ANSWER:
No;
7. 11 mm, 21 mm, 16 mm
SOLUTION:
ANSWER:
Yes; 11 + 21 > 16, 11 + 16 > 21, and 16 + 21 > 11
8. 9.9 cm, 1.1 cm, 8.2 cm
ANSWER:
No;
9. 2.1 in., 4.2 in., 7.9 in.