Question

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geometry
name ______________________ id: 1
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triangle inequality theorem - independent pract. date __________ team __
state if the three numbers can be the measures of the sides of a triangle.

1. 12, 10, 25
2. 21, 11, 9
3. 8, 13, 7
4. 13, 9, 6
5. 12, 3, 9
6. 2, 7, 7

two sides of a triangle have the following measures. find the range of possible measures for
the third side.

1. 7, 12
2. 8, 8
3. 9, 12
4. 9, 8
5. 10, 8
6. 12, 8

Explanation:

Step1: Apply Triangle Inequality Theorem

For three side lengths $a, b, c$ (where $c$ is the largest), check if $a + b > c$.
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Problem 1: 12, 10, 25

Step1: Identify largest side

Largest side = 25

Step2: Sum smaller sides

$12 + 10 = 22$

Step3: Compare sum to largest

$22
gtr 25$
---

Problem 2: 21, 11, 9

Step1: Identify largest side

Largest side = 21

Step2: Sum smaller sides

$11 + 9 = 20$

Step3: Compare sum to largest

$20
gtr 21$
---

Problem 3: 8, 13, 7

Step1: Identify largest side

Largest side = 13

Step2: Sum smaller sides

$8 + 7 = 15$

Step3: Compare sum to largest

$15 > 13$
---

Problem 4: 13, 9, 6

Step1: Identify largest side

Largest side = 13

Step2: Sum smaller sides

$9 + 6 = 15$

Step3: Compare sum to largest

$15 > 13$
---

Problem 5: 12, 3, 9

Step1: Identify largest side

Largest side = 12

Step2: Sum smaller sides

$3 + 9 = 12$

Step3: Compare sum to largest

$12
gtr 12$
---

Problem 6: 2, 7, 7

Step1: Identify largest side

Largest side = 7

Step2: Sum smaller sides

$2 + 7 = 9$

Step3: Compare sum to largest

$9 > 7$
---

Problem 7: 7, 12 (find third side $x$)

Step1: Use inequality rules

For sides $a, b, x$: $|a - b| < x < a + b$

Step2: Calculate bounds

$|12 - 7| = 5$, $12 + 7 = 19$

Step3: Write range

$5 < x < 19$
---

Problem 8: 8, 8 (find third side $x$)

Step1: Use inequality rules

$|8 - 8| < x < 8 + 8$

Step2: Calculate bounds

$|8 - 8| = 0$, $8 + 8 = 16$

Step3: Write range

$0 < x < 16$
---

Problem 9: 9, 12 (find third side $x$)

Step1: Use inequality rules

$|12 - 9| < x < 12 + 9$

Step2: Calculate bounds

$|12 - 9| = 3$, $12 + 9 = 21$

Step3: Write range

$3 < x < 21$
---

Problem 10: 9, 8 (find third side $x$)

Step1: Use inequality rules

$|9 - 8| < x < 9 + 8$

Step2: Calculate bounds

$|9 - 8| = 1$, $9 + 8 = 17$

Step3: Write range

$1 < x < 17$
---

Problem 11: 10, 8 (find third side $x$)

Step1: Use inequality rules

$|10 - 8| < x < 10 + 8$

Step2: Calculate bounds

$|10 - 8| = 2$, $10 + 8 = 18$

Step3: Write range

$2 < x < 18$
---

Problem 12: 12, 8 (find third side $x$)

Step1: Use inequality rules

$|12 - 8| < x < 12 + 8$

Step2: Calculate bounds

$|12 - 8| = 4$, $12 + 8 = 20$

Step3: Write range

$4 < x < 20$

Answer:

1. No
2. No
3. Yes
4. Yes
5. No
6. Yes
7. $5 < x < 19$
8. $0 < x < 16$
9. $3 < x < 21$
10. $1 < x < 17$
11. $2 < x < 18$
12. $4 < x < 20$