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Two distinct intersecting lines cannot b...

Two distinct intersecting lines cannot be parallel to the same line.

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To determine whether the statement "Two distinct intersecting lines cannot be parallel to the same line" is true or false, we can analyze the definitions and properties of lines in Euclidean geometry. ### Step-by-Step Solution: 1. **Understanding the Terms**: - **Distinct Lines**: These are lines that are not the same; they do not coincide. - **Intersecting Lines**: These are lines that cross each other at a point. - **Parallel Lines**: These are lines that never meet, no matter how far they are extended. 2. **Analyzing the Statement**: - The statement claims that two distinct lines that intersect cannot both be parallel to the same line. 3. **Visualizing the Scenario**: - Let's assume we have two distinct lines, Line A and Line B, that intersect at a point. - If we introduce a third line, Line C, we need to check if both Line A and Line B can be parallel to Line C. 4. **Applying the Definition of Parallel Lines**: - If Line A is parallel to Line C, it means they will never intersect. - If Line B is also parallel to Line C, it too will never intersect with Line C. 5. **Conclusion**: - Since Line A and Line B are distinct lines that intersect, they cannot both be parallel to Line C. If one line is parallel to another, they cannot intersect. - Therefore, the statement "Two distinct intersecting lines cannot be parallel to the same line" is **True**. ### Final Answer: The statement is **True**.
To determine whether the statement "Two distinct intersecting lines cannot be parallel to the same line" is true or false, we can analyze the definitions and properties of lines in Euclidean geometry. ### Step-by-Step Solution: 1. **Understanding the Terms**: - **Distinct Lines**: These are lines that are not the same; they do not coincide. - **Intersecting Lines**: These are lines that cross each other at a point. - **Parallel Lines**: These are lines that never meet, no matter how far they are extended. ...
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