Read the following two statements. Then use the Law of Syllogism to draw a conclusion. If three points lie on the same line, they are collinear. If three points are collinear, they lie in the same plane. If three points lie in the same line, they lie in the same plane. If three points do not lie in the same plane, they do not lie on the same line. The three points are collinear. The three points lie in the same plane.
Based on the given statements:
1. If three points lie on the same line, they are collinear.
2. If three points are collinear, they lie in the same plane.
We can use the Law of Syllogism to draw the conclusion:
3. If three points lie on the same line, they lie in the same plane.
Given:
4. The three points are collinear.
5. The three points lie in the same plane.
Using the Law of Syllogism, we can conclude:
6. The three points lie in the same plane since they are collinear.
To draw a conclusion using the Law of Syllogism, let's analyze the given statements:
1. If three points lie on the same line, they are collinear.
2. If three points are collinear, they lie in the same plane.
3. If three points lie in the same line, they lie in the same plane.
4. If three points do not lie in the same plane, they do not lie on the same line.
Given the following conclusions:
1. The three points are collinear.
2. The three points lie in the same plane.
Using the Law of Syllogism, we can combine statements 1 and 2 as follows:
Statement 1: If three points lie on the same line, they are collinear.
Statement 2: If three points are collinear, they lie in the same plane.
Combined Conclusion using Law of Syllogism:
If three points lie on the same line, they lie in the same plane.
Therefore, the conclusion is that if three points are collinear, they lie in the same plane.
To draw a conclusion using the Law of Syllogism, we need to analyze the given statements and find a valid chain of reasoning.
Let's break down the given statements:
Statement 1: "If three points lie on the same line, they are collinear."
Statement 2: "If three points are collinear, they lie in the same plane."
Statement 3: "If three points lie in the same line, they lie in the same plane."
Statement 4: "If three points do not lie in the same plane, they do not lie on the same line."
The goal is to draw a conclusion based on the information provided. We have two statements left after breaking down the given information:
Statement 5: "The three points are collinear."
Statement 6: "The three points lie in the same plane."
Using the Law of Syllogism, we can deduce that if statement 1 is true and statement 5 is true, then it follows that statement 2 is true. Similarly, if statement 3 is true and statement 2 is true, then it follows that statement 6 is true.
Therefore, we can conclude that since the three points are collinear (statement 5 is true) and if three points are collinear, they lie in the same plane (statement 2 is true), then it follows that the three points also lie in the same plane (statement 6 is true).
In summary, based on the given statements and applying the Law of Syllogism, we can draw the conclusion that the three points are both collinear and lie in the same plane.