Segment — Geometry, what it means and where it is taught
Two endpoints and everything between them. Written AB.
Taught in Geometry.
Where it is taught
What uses it later
This idea is needed for:
- Polygon — A closed figure made of straight segments that meet only at endpoints.
- Diagonal — A segment joining two non-adjacent vertices.
- Chord — A segment joining two points on the circle.
Practise this idea
16 questions in the course bank use Segment, in Geometric Construction, Dilations & Similarity, Distance on the Coordinate Plane, Definitions, Postulates & Reasoning, How to Write a Proof, Coordinate Geometry Proofs. The first 8 are below; the rest are in those units.
Problem 1
Can segments of length 5, 7 and 13 form a triangle?
- Yes
- No
Worked answer
No
5 + 7 = 12
12 < 13
The two short sides cannot reach across, so no triangle exists.
Problem 2
Can segments of length 4, 9 and 11 form a triangle?
- Yes
- No
Worked answer
Yes
4 + 9 = 13 > 11 ✓
A triangle is possible.
Problem 3
Dilate the segment from (2, 2) to (6, 4) by a factor of 3 about the origin. Give the two image points.
Worked answer
(6, 6) and (18, 12)
(2,2) → (6,6)
(6,4) → (18,12)
Problem 4
Find the distance between (2, 5) and (2, 12).
Worked answer
7
It is a vertical segment
12 - 5 = 7
No square root needed
Problem 5
The distance from (2, 3) to (2, k) is 9, with k > 3. Find k.
Worked answer
12
|k - 3| = 9
k - 3 = 9 since k > 3
k = 12
Problem 6
The midpoint of a segment is (0, 0) and one endpoint is (-6, 8). Find the other endpoint.
Worked answer
(6, -8)
-6 + x2 = 0, so x = 6
8 + y2 = 0, so y = -8
Problem 7
Write the symbol for the segment with endpoints A and B.
Worked answer
AB with a bar
AB
The bar means a segment, not a length.
Problem 8
B is between A and C. AB = 7 and BC = 12. Find AC.
Worked answer
19
AB + BC = AC
7 + 12 = 19