https://file.aiquickdraw.com/mathbot/file/1727412019384fzcvoxjg.jpg

Let's solve the proof in the image you uploaded. The task is to prove \( QS = RT \) given that \( QR = ST \), with a two-column proof.

### Setup:
- **Given:** \( QR = ST \)
- **To Prove:** \( QS = RT \)

The diagram shows points \( Q, R, S, T \) on a line with segments labeled \( QR \) and \( ST \). The goal is to prove that the lengths of segments \( QS \) and \( RT \) are equal.

### Two-Column Proof:

| **Statements**                         | **Reasons**                                |
|----------------------------------------|--------------------------------------------|
| 1. \( QR = ST \)                       | Given                                      |
| 2. \( QS = QR + RS \)                  | Segment Addition Postulate                 |
| 3. \( RT = RS + ST \)                  | Segment Addition Postulate                 |
| 4. \( QR = ST \)                       | Given (restated)                           |
| 5. \( QS = RT \)                       | Substitution from steps 2, 3, and 4        |

### Explanation:
1. The first statement is the given information: \( QR = ST \).
2. Using the **Segment Addition Postulate**, we express \( QS \) as the sum of segments \( QR \) and \( RS \).
3. Similarly, using the same postulate, we express \( RT \) as the sum of \( RS \) and \( ST \).
4. We substitute the given condition \( QR = ST \) from step 1 into the equations for \( QS \) and \( RT \).
5. Finally, by substituting \( QR \) for \( ST \) in the expression for \( RT \), we find that \( QS = RT \), which proves the statement.

Would you like any details or further clarifications?

Here are 5 related questions:
1. What is the **Segment Addition Postulate**?
2. Why is \( QS = QR + RS \) valid for a straight line?
3. Can this method be used for non-collinear points?
4. How does substitution work in geometric proofs?
5. Why do we restate the given information in the proof?

**Tip:** Always restate given information when writing a proof. This keeps your argument clear and ensures you're using all available information.

Prove QS = RT given QR = ST with points Q, R, S, and T on a line segment.

This geometric proof involves proving QS = RT given QR = ST using the Segment Addition Postulate. Explore a step-by-step guide to solving this high school-level problem, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation