To bisect a segment is to divide it into two congruent parts — two parts with the same measure. The point where the division happens is the midpoint, and anything that does the dividing — a point, a line, a ray, another segment, or a plane — is a segment bisector. That one relationship drives all of the algebra on this page: the two halves are equal, and the whole segment is twice a half. Notice what bisection does not say: a point between two others is usually not a midpoint, and a bisector of one segment says nothing about the parts of another segment.
In the figure, line k intersects segment AB at point M. Because M is the midpoint, the two halves have the same measure — the matching tick marks show that the halves are congruent — and the whole segment is twice a half.
What you are looking at: Segment AB with a point M that can slide along it. The purple line through M moves with the point — it is a candidate bisector: it bisects the segment only when it intersects the segment at its midpoint. The measures of the two parts, AM and MB, are written under the segment.
What to do: Drag the orange handle on point M along the segment. Try to stop M at the exact midpoint of the segment. Point M stays on the segment — a drag that would push it past an endpoint is refused.
What to notice: When the two parts are exactly equal, matching tick marks appear on the two halves and the readout turns green: M is the midpoint, the halves are congruent (equal in measure), and the whole segment is twice a half. When the parts are not equal, there are no tick marks and no green — between does not mean in the middle.
New Segment button — starts a segment with a different total length, with point M back at a starting spot that is not the midpoint, so you can hunt for the new midpoint.
What to do: Each problem shows a figure and asks you to identify the midpoint or the bisector, or to decide what must be true. Pick an answer: the figure element your choice names lights up — in gold if the choice is right, as a grey dashed ghost if it is not — so you can see what the choice means. A first miss gives a hint and another try, with the missed choice removed. A second miss names the correct choice and explains it. Watch the tick marks: matching tick marks on two parts mean those parts are congruent (equal in measure).
Continue button — moves to the next problem after a problem is finished. New Item button — shows the next problem; the problems take turns in order, and the problem number is shown with the question.
What to do: Each problem gives you a segment and its midpoint, with some measures written as expressions. Work in three steps: (1) choose the equation to use to solve the problem, (2) solve the equation for the variable, 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. 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 definition first, with its equation written in the figure's own names, then substitution, then solving — and substituting back whenever the question asks for the measure of a part or the whole.
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.
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 Bisector — Mr. J Geometry. All activities on this page run entirely in your browser.