Question

1. use the law of detachment or syllogism to draw a conclusion from the given statements.

· given: if two lines intersect and form right angles, then the lines are perpendicular.

· given: if two lines are perpendicular, then they intersect and form 90 degrees angles.

· conclusion:

Explanation:

Step1: Identify the form of reasoning

We use the Law of Syllogism. The Law of Syllogism states that if \(p
ightarrow q\) and \(q
ightarrow r\), then \(p
ightarrow r\). Here, let \(p\) be "two lines intersect and form right - angles", \(q\) be "the lines are perpendicular", and \(r\) be "they intersect and form 90 degrees angles".

Step2: Draw the conclusion

Since \(p
ightarrow q\) and \(q
ightarrow r\), by the Law of Syllogism, we can conclude that if two lines intersect and form right angles, then they intersect and form 90 degrees angles.

Answer:

If two lines intersect and form right angles, then they intersect and form 90 degrees angles.