Between

Elementary SchoolMiddle School

Definition

When you have a line with endpoints X and Z, a point Y is between points X and Z if it is on the XZ line segment. The idea of a number being between two other numbers is used in Euclid's proofs.

Worked examples

\(X\)———\(Y\)———\(Z\)

Point \(Y\) is between \(X\) and \(Z\) because it lies on segment \(XZ\).

\(5\) is between \(2\) and \(9\) because \(2 < 5 < 9\)

On the number line, a number is between two others when it falls strictly inside their interval.

Common mistakes

Point \(Y\) is between \(X\) and \(Z\) if it is anywhere near the line → Point \(Y\) must lie exactly on segment \(XZ\) Being 'between' requires the point to be on the line segment itself, not just close to it.
\(3\) is between \(3\) and \(7\) → \(3\) is an endpoint, not between \(3\) and \(7\) 'Between' means strictly inside the interval; endpoints are not between themselves and another point.
If \(Y\) is between \(X\) and \(Z\), then \(XY + YZ \ne XZ\) → If \(Y\) is between \(X\) and \(Z\), then \(XY + YZ = XZ\) A point between two others divides the segment so the sum of the parts equals the whole (segment addition postulate).

Where you'll use it next

The between concept is foundational for segment addition, midpoint formulas, and inequality proofs in geometry. You'll also use it in algebra when solving compound inequalities and analyzing intervals on the number line.

Found in 1 StudyPug lesson

Comparing and Ordering Rational Numbers

Grade 9 Math

Convert rational numbers to a common form, then read their order from a number line.

9th Grade9th