When a point lies between two other points on the same line, the two smaller segments add up to the whole segment. That one idea turns pictures into equations: add the parts, set the sum equal to the whole, and solve. The key word is between — a point between two others is somewhere along the segment joining them. Between does not mean in the middle, and it does not mean the point is a midpoint: most points between two others split the segment into two parts of different lengths.
When a point lies between two other points on the same line, the two smaller segments add up to the whole segment. That is the Segment Addition Postulate, and it turns pictures into equations: add the parts, set the sum equal to the whole, and solve. The key word is between — a point between two others is somewhere along the segment, not necessarily in the middle.
What you are looking at: Three collinear points on a number line. Point B is between points A and C, so segment AC is split into two parts, AB and BC. The measure of each part is written under the line.
What to do: Drag the orange handle on point B to slide B between A and C. Drag the purple handles on points A and C to move the ends. Each point must stay on the number line, and B must stay strictly between A and C — a drag that would push B onto or past an end, or push an end onto or past B, is refused.
What to notice: B is deliberately not placed in the middle. However you drag, the two parts always add to the whole: AB + BC = AC, with the actual numbers shown in the readout. B is the midpoint only in the special position where the two parts happen to be equal.
What to do: Each problem gives you a segment split into two parts by a point between its ends. Work in three steps: (1) choose the equation to use to solve the problem, (2) solve the equation or find the missing measure, and (3) report the measure the question actually asks for. The gold highlight in the diagram always marks the part the current step asks about, and a part solved in an earlier step is labeled with its found measure. Each choice you pick slides a marker along the segment to the position that choice describes, whether the choice is right or wrong, so you can see what the choice means; a missed choice is shown as a dashed amber marker. A first miss gives a hint and another try, with the missed choice removed. A second miss on a step names the correct choice and explains it, and the activity then moves on. When all three steps are complete, the full worked solution appears. Every worked solution is written the way work is done in class: the Segment Addition Postulate statement first, then substitution, then solving — and substituting back whenever the question asks for the measure of a part.
Continue button — moves to the next step after a step is finished. New Item button — shows the next problem; the problems take turns in order, and the problem number is shown with the step question.
What you are looking at: This is a separate challenge activity. The problems here work exactly like the ones above — a point between two others, parts adding to the whole — but one or more of the given measures leads to an equation with an x² term, and the whole measure can come out far larger than either part. Each problem states which value of x to use.
What to do: Work in the same three steps: (1) choose the equation to use to solve the problem, (2) solve for the value of x the problem asks you to use, and (3) substitute back to report the measure the question actually asks for. The gold highlight in the diagram always marks the part the current step asks about, and a part solved in an earlier step is labeled with its found measure. Choices, hints, misses, and the worked solution behave exactly as in the activity above. Every worked solution follows the same order: the Segment Addition Postulate statement, then substitution, then solving.
Continue button — moves to the next step after a step is finished. New Item button — shows the next challenge problem; the problems take turns in order, and the problem number is shown with the step question.
Ready to practice? Work through these six questions, one at a time. If your first answer is wrong, you will get a hint and another try; the full explanation appears once you answer correctly, or after a second miss. Your score counts first-try answers.
Segment Addition — Mr. J Geometry. All activities on this page run entirely in your browser.