Math Problem Statement

Find the length of segment AB, given that BC = 10 and AC = 12, using the segment addition axiom.

Solution

The image shows a geometry problem involving the segment addition axiom. The given diagram shows a line segment with points AA, BB, and CC, where:

  • AB=?AB = ? (unknown)
  • BC=10BC = 10
  • AC=12AC = 12

To find the length of segment ABAB, we can use the segment addition axiom, which states:

AB+BC=ACAB + BC = AC

Substituting the known values:

AB+10=12AB + 10 = 12

Solving for ABAB:

AB=1210=2AB = 12 - 10 = 2

Thus, the length of segment ABAB is 2 units.


Would you like further explanation or details? Here are five related questions for further exploration:

  1. What is the segment addition axiom in geometry?
  2. How would the solution change if BCBC were longer than ACAC?
  3. What happens if the total segment length ACAC is not greater than BCBC?
  4. Can you apply the segment addition axiom in three-dimensional geometry?
  5. How can you use the segment addition axiom to solve problems involving multiple points on a line?

Tip: Always double-check given values and their relationships when using geometric axioms to ensure accurate solutions.

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Math Problem Analysis

Mathematical Concepts

Geometry
Segment Addition Axiom
Linear Equations

Formulas

AB + BC = AC

Theorems

Segment Addition Axiom

Suitable Grade Level

Grades 6-8