Additive property of length

Learning Objectives Define the Segment Addition Postulate and the concept of betweenness of points. Apply the additive property of length to calculate the length of a segment given the lengths of its component parts. Set up and solve algebraic equations to find unknown segment lengths. Use segment lengths to determine if three points are collinear. Correctly use the Segment Addition Postulate as a justification in geometric proofs. Differentiate between the notation for a line segment (e.g., \overline{AB}) and its length (e.g., AB). Ever planned a road trip with a stop in the middle? How do you find the total distance? 🗺️ The simple act of adding the two legs of the journey is a real-world example of the additive property of length! This tutorial explores the Segment Additi...

TermDefinitionExample PointA specific location in space. It has no dimension (no length, width, or height) and is represented by a dot.In the diagram, A, B, and C are all points. Line SegmentA part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. It is denoted by \overline{AB}.A piece of a ruler from the 2 cm mark to the 5 cm mark is a line segment. Length of a SegmentThe distance between the endpoints of a line segment. It is a positive number. The length of \overline{AB} is denoted by AB (without the bar).If \overline{AB} spans from x=3 to x=8 on a number line, its length AB is 5 units. Collinear PointsPoints that lie on the same straight line.If you can draw a single straight line that passes through points P, Q, and R, t...

Segment Addition Postulate If B is a point on \overline{AC} between A and C, then AB + BC = AC. This postulate allows you to find the total length of a segment by adding the lengths of its smaller, adjacent, and collinear parts. It is the core of the additive property of length. Converse of the Segment Addition Postulate If three points A, B, and C satisfy the equation AB + BC = AC, then B must lie on the line segment \overline{AC}. This rule is used to prove that three points are collinear. If the sum of the two smaller distances equals the largest distance, the points form a single straight line segment.