What is law of detachment in geometry?

The Law of Detachment is a principle in geometry used to make logical deductions from given statements or premises. It states that if two conditional statements are given, and the hypothesis (the "if" part) of the first conditional matches the conclusion (the "then" part) of the second conditional, then the conclusion of the first conditional can be validly deduced.

Symbolically, the Law of Detachment can be expressed as follows:

If p --> q is true, and p is true, then q is true.

This is often written as:

If p --> q and p, then q.

For example, given the statements:

• If an angle measures 90 degrees, then it is a right angle. (p --> q)
• Angle A measures 90 degrees. (p)

By applying the Law of Detachment, we can deduce that "Angle A is a right angle" (q) is also true.

The Law of Detachment is closely related to the concept of an implication or conditional statement. It allows us to draw logical conclusions from given statements and can be applied in various geometric proofs. Understanding this law helps in developing mathematical reasoning skills and making valid deductions in geometric arguments.