How to Construct a Segment that is Twice as Long as PQ with the Segment Addition Postulate

Explanation:

To construct a segment that is twice as long as segment PQ, we use a ruler to measure the length of PQ and then double that measurement to define segment AB. The Segment Addition Postulate can be used to justify this by stating that if points A, B, and P are collinear in that order, then AP + PB = AB.

In this case, if we consider point P as the midpoint of segment AB, then AP = PB = PQ. Hence, AB = AP + PB = PQ + PQ = 2PQ which verifies that AB is indeed twice as long as PQ.

This showcases the geometric property of line segments defined by the Segment Addition Postulate, demonstrating how measuring segments and applying mathematical rules enable us to accurately construct proportions in geometry.