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

How can we create a segment that is double the length of another using the Segment Addition Postulate? To create a segment that is double the length of another, measure the original segment then double that measurement. The Segment Addition Postulate justifies this by noting that if point P is the midpoint of segment AB, AB is twice as long as AP (or PB), thereby AB = 2PQ.

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.

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