contestada

17. Determine if the following segments can or cannot be a triangle.

3 m., 4 m., and 1 m.
⬜ Yes ⬜ No


12 ft., 3 ft., and 11 ft.
⬜ Yes ⬜ No
24 in., 13 in., and 5 in.
⬜ Yes ⬜ No


9.81 m., 16 m., and 6.19 m.
⬜ Yes ⬜ No
5 yds., 13 yds., and 10 yds.
⬜ Yes ⬜ No


2.5 cm., 2.5 cm., and 2.5 cm.
⬜ Yes ⬜ No
6 mm., 4 mm., and 9 mm.
⬜ Yes ⬜ No


7 ft., 7 ft., and 7 ft.
⬜ Yes ⬜ No

17 Determine if the following segments can or cannot be a triangle 3 m 4 m and 1 m Yes No 12 ft 3 ft and 11 ft Yes No 24 in 13 in and 5 in Yes No 981 m 16 m and class=
17 Determine if the following segments can or cannot be a triangle 3 m 4 m and 1 m Yes No 12 ft 3 ft and 11 ft Yes No 24 in 13 in and 5 in Yes No 981 m 16 m and class=
17 Determine if the following segments can or cannot be a triangle 3 m 4 m and 1 m Yes No 12 ft 3 ft and 11 ft Yes No 24 in 13 in and 5 in Yes No 981 m 16 m and class=
17 Determine if the following segments can or cannot be a triangle 3 m 4 m and 1 m Yes No 12 ft 3 ft and 11 ft Yes No 24 in 13 in and 5 in Yes No 981 m 16 m and class=
17 Determine if the following segments can or cannot be a triangle 3 m 4 m and 1 m Yes No 12 ft 3 ft and 11 ft Yes No 24 in 13 in and 5 in Yes No 981 m 16 m and class=

Respuesta :

hockeykhloe

Answer:

Step-by-step 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.

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