To find LP when LR = 12 and PR = 4, we apply the Segment Addition Postulate, which states that if a point P lies on segment LR, then LP + PR = LR. Substituting the given values, we get LP + 4 = 12. Solving for LP, we subtract 4 from both sides and obtain LP = 12 - 4, which simplifies to LP = 8. Therefore, LP is 8, according to the subtraction property of equality.

Correct, to find the length of segment LP when you know the lengths of the entire segment LR and a portion of it, PR, you can use the Segment Addition Postulate. This principle applies when you have three points—L, P, and R—that lie on the same straight line, with point P being between L and R. According to this postulate, if you add the lengths of LP and PR, it should equal the total length LR.

Given: LR = 12 PR = 4 LP + PR = LR

Substitute the known values into the equation: LP + 4 = 12

To solve for LP, follow these steps: 1. Subtract 4 from both sides of the equation to isolate LP on one side: LP + 4 - 4 = 12 - 4 2. This simplifies to: LP = 8

So the length of segment LP is 8 units. This subtraction process is guided by the subtraction property of equality, which states that if you subtract the same value from both sides of an equation, the equality remains true.