https://file.aiquickdraw.com/mathbot/file/1728762792282brvcqsgu.jpg

To determine the correct postulate that supports the statement "Lines \( n \) and \( l \) intersect at point \( K \)," we need to recall some basic postulates of geometry.

The options given correspond to commonly used postulates in geometry:

- **Postulate 2.1:** Through any two points, there is exactly one line.
- **Postulate 2.3:** If two lines intersect, then they intersect in exactly one point.
- **Postulate 2.6:** If two planes intersect, then their intersection is a line.
- **Postulate 2.7:** Through any three non-collinear points, there is exactly one plane.

The given statement is about the intersection of two lines at a single point. Therefore, the correct postulate is **Postulate 2.3**: "If two lines intersect, then they intersect in exactly one point."

Thus, the answer is **B. 2.3**.

Would you like more details or have any further questions? 

Here are five related questions to deepen your understanding:
1. What is the definition of a postulate in geometry?
2. Can two distinct lines intersect at more than one point? Why or why not?
3. How is Postulate 2.1 different from Postulate 2.3?
4. What postulate would apply if lines did not intersect but were parallel?
5. How do the concepts of lines, points, and planes interact in three-dimensional space?

**Tip:** Remember that a postulate is a statement accepted as true without proof, serving as a foundational principle in geometry.

State the postulate that can be used to show each statement is true. Lines n and l intersect at point K.

Explore the geometry postulate 2.3, which states that two lines intersect at exactly one point. This problem illustrates the concept with lines n and l intersecting at point K. 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