To solve the problem, we need to identify the correct term that matches the given logical definition: "If [tex]\( p \rightarrow q \)[/tex] is true, and [tex]\( p \)[/tex] is true, then [tex]\( q \)[/tex] is true."
Let's briefly review each of the given options to understand what they mean:
1. Segment Addition Postulate: This postulate states that if a point lies on a line segment, the total length of the segment is the sum of the lengths of the two parts created by the point. This is related to geometry and doesn't fit the description.
2. Vertical Angle Postulate: This postulate asserts that vertical (opposite) angles are congruent. This is related to angles formed by intersecting lines and doesn't fit the description.
3. Law of Syllogism: This law states that if [tex]\( p \rightarrow q \)[/tex] and [tex]\( q \rightarrow r \)[/tex] are true, then [tex]\( p \rightarrow r \)[/tex] is also true. Although this pertains to logical connections, it is not the one matching the given definition.
4. Linear Pair Postulate: This postulate states that if two angles form a linear pair (meaning they are adjacent and their non-common sides form a straight line), then they are supplementary (sum up to 180 degrees). This is related to geometry and doesn't fit the description.
5. Angle Addition Postulate: This postulate states that if an angle is split into two smaller angles by a ray, the measure of the whole angle is the sum of the measures of the two smaller angles. This is related to the angles’ measures and doesn't fit the description.
6. Law of Detachment: This law states that if [tex]\( p \rightarrow q \)[/tex] is true (if p implies q), and [tex]\( p \)[/tex] is true, then [tex]\( q \)[/tex] must also be true. This exactly corresponds to the given definition.
After reviewing all options and definitions, the appropriate match for the definition "If [tex]\( p \rightarrow q \)[/tex] is true, and [tex]\( p \)[/tex] is true, then [tex]\( q \)[/tex] is true" is the Law of Detachment.
Therefore, the correct answer is:
Law of Detachment
So, we select option 6: Law of Detachment.
