https://file.aiquickdraw.com/mathbot/file/1730299082897yukzwa7v.jpg

To solve this problem, we need to determine the length of \( SU \) in triangle \( STU \), which is formed by connecting the midpoints of the sides of triangle \( PQR \).

### Step-by-Step Solution
1. **Identify Midpoints**: Given that \( S \), \( T \), and \( U \) are midpoints of sides \( PQ \), \( QR \), and \( RP \), respectively, we know that triangle \( STU \) is the medial triangle of \( PQR \). In a medial triangle, each side of the smaller triangle is parallel to and half the length of the corresponding side of the original triangle.

2. **Determine Corresponding Side**: The side \( SU \) in triangle \( STU \) corresponds to side \( PR \) in triangle \( PQR \). By the midpoint properties, \( SU \) will be half the length of \( PR \).

3. **Calculate \( PR \)**: In the diagram, side \( PR \) is given as \( 8 \). Since \( SU \) is half of \( PR \),
   \[
   SU = \frac{PR}{2} = \frac{8}{2} = 4.
   \]

### Answer
The length of \( SU \) is \( \boxed{4} \).

Would you like further details or explanations on this problem? Here are some related questions for further exploration:

1. How do you find the length of other sides in the medial triangle \( STU \)?
2. What are the properties of a medial triangle in any given triangle?
3. How does the concept of parallel lines apply to the sides of a medial triangle?
4. Can this method be used for any triangle, regardless of its type?
5. How would this problem change if \( PQR \) were not a triangle but a different polygon?

**Tip**: Remember, in a triangle, connecting the midpoints of the sides always results in a medial triangle, with each side equal to half of the corresponding side in the larger triangle.

Triangle STU is formed by connecting the midpoints of the side of triangle PQR. The lengths of the sides of triangle PQR are shown. What is the length of SU?

Learn how to find the length of SU in the medial triangle STU, formed by connecting midpoints in triangle PQR. This problem demonstrates the properties of medial triangles and midpoint theorem, with a step-by-step solution. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation