Unit 1: Geometry Basics Homework 2: Segment addition

The Segment Addition Postulate is a fundamental rule in geometry that helps calculate the total length of a line segment made up of two smaller segments. It states:

If a point B lies on a line segment between two other points, A and $C$, then the total length of AC is the sum of the lengths of AB and $BC$. Mathematically:

C=AB+BC

Example 1:

If $AB=5\text{cm}$ and BC=8 CM, find the total length of AC:

AC = AB + BC = 5 + 8 = 13 cm

Example 2:

If the total segment $AC=20\text{cm}$ and one smaller segment $=12\text{cm}$, find the length of $BC$:

BC=AC−AB=20−12=8cm

Steps:

1. Understand the diagram: Identify the segments involved.
2. Use the postulate: Write the equation $AB+BC$.
3. Solve for the unknown: Rearrange as needed to find the missing segment length.