Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Determine each segment length in right triangle A⁢B⁢C.

14

14⁢2

7⁢3

14⁢3

7

7⁢2

B⁢C

B⁢D

To determine the segment lengths in the right triangle \( ABC \), let's assume the triangle is a right triangle with \( AB \) and \( AC \) as the legs and \( BC \) as the hypotenuse. 

Since you provided the following tile options:
- \( 14 \)
- \( 14\sqrt{2} \)
- \( 7\sqrt{3} \)
- \( 14\sqrt{3} \)
- \( 7 \)
- \( 7\sqrt{2} \)

We'll assume the common right triangle relationships and the Pythagorean theorem apply here. 

1. **Identify the legs**: Let's say \( AB = 14 \) and \( AC = 14\sqrt{2} \).
2. **Calculate the hypotenuse**: Using the Pythagorean theorem:
   \[
   BC = \sqrt{AB^2 + AC^2} = \sqrt{(14)^2 + (14\sqrt{2})^2} = \sqrt{196 + 392} = \sqrt{588} = 14\sqrt{3}
   \]

### Resulting Lengths:
- \( AB = 14 \)
- \( AC = 14\sqrt{2} \)
- \( BC = 14\sqrt{3} \)

### Not Used:
- \( 7\sqrt{3} \), \( 7 \), \( 7\sqrt{2} \)

Would you like further details on the calculations or explanations? Here are some follow-up questions to consider:

1. How do you determine the relationships between the sides in a right triangle?
2. Can you explain the Pythagorean theorem with an example?
3. What other geometric shapes use similar segment relationships?
4. How would the lengths change if different values were assigned to the legs?
5. Are there any specific applications of right triangles in real-world scenarios?

**Tip**: Always verify the conditions of a triangle (like the Pythagorean theorem) when working with right triangles to ensure accurate lengths and relationships.

Determine each segment length in right triangle A⁢B⁢C.

Explore how to determine segment lengths in right triangle ABC using the Pythagorean theorem. Given lengths include 14, 14√2, and 14√3. Ideal for students in Grades 7-9 learning about geometry.

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