9 pts
 

1.3.5 cool down.png

Select the two options that could be measurements of Triangle Z.

Group of answer choices

8, 11, 14

100, 175, 250

6, 9, 11

6, 12, 15

8, 14, 20


To determine which of the options could represent the side lengths of a valid triangle, we can apply the **Triangle Inequality Theorem**. This theorem states that, for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Let's test each set:

### 1. \( 8, 11, 14 \)
- \( 8 + 11 = 19 \), and \( 19 > 14 \)
- \( 8 + 14 = 22 \), and \( 22 > 11 \)
- \( 11 + 14 = 25 \), and \( 25 > 8 \)

Since all conditions are satisfied, this is a valid triangle.

### 2. \( 100, 175, 250 \)
- \( 100 + 175 = 275 \), and \( 275 > 250 \)
- \( 100 + 250 = 350 \), and \( 350 > 175 \)
- \( 175 + 250 = 425 \), and \( 425 > 100 \)

All conditions are satisfied, so this is a valid triangle.

### 3. \( 6, 9, 11 \)
- \( 6 + 9 = 15 \), and \( 15 > 11 \)
- \( 6 + 11 = 17 \), and \( 17 > 9 \)
- \( 9 + 11 = 20 \), and \( 20 > 6 \)

This set satisfies the conditions, so it is a valid triangle.

### 4. \( 6, 12, 15 \)
- \( 6 + 12 = 18 \), and \( 18 > 15 \)
- \( 6 + 15 = 21 \), and \( 21 > 12 \)
- \( 12 + 15 = 27 \), and \( 27 > 6 \)

All conditions are satisfied, so this is a valid triangle.

### 5. \( 8, 14, 20 \)
- \( 8 + 14 = 22 \), and \( 22 > 20 \)
- \( 8 + 20 = 28 \), and \( 28 > 14 \)
- \( 14 + 20 = 34 \), and \( 34 > 8 \)

This set satisfies the conditions, so it is also a valid triangle.

### Conclusion:
The two valid triangles are:

- \( 8, 11, 14 \)
- \( 6, 9, 11 \)

Would you like further details on any of these concepts?

---

Here are five related questions:
1. How does the Triangle Inequality Theorem apply to different types of triangles?
2. What are the properties of an equilateral triangle, and how do they relate to side lengths?
3. How would the Triangle Inequality Theorem work for right triangles?
4. Can a triangle have side lengths that are all equal? What kind of triangle is that?
5. How does the Pythagorean theorem relate to the side lengths of a right triangle?

**Tip:** Always check if side lengths satisfy the Triangle Inequality Theorem to confirm if a set of numbers can form a triangle.

Select the two options that could be measurements of Triangle Z.

Group of answer choices:

- 8, 11, 14
- 100, 175, 250
- 6, 9, 11
- 6, 12, 15
- 8, 14, 20

Explore how to determine if side lengths can form a valid triangle using the Triangle Inequality Theorem. We analyze options like 8, 11, 14 and 6, 9, 11 to explain which sets are valid. This concept is ideal for students in Grades 8-10 studying geometry and triangle properties.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation