In this lesson
What lines, rays, segments, angles, and polygons are
In geometry, four small drawings carry four different meanings:
- A straight line extends forever in both directions. It has no
endpoints. We name it with two points it passes through and a
double-arrow above the letters:
AB⃡. - A ray starts at one point, the endpoint, and extends
forever in one direction. We name it with the endpoint first and
a right-arrow above:
AB⃗. The endpoint A is fixed; the ray runs through B and keeps going. - A line segment is the piece of a straight line between two
given points. It has both endpoints. The notation is
A̅B̅, a bar above the letters. - An angle is what you get when two rays (or segments, or lines)
share a vertex. The notation is
∠ABC: three letters, with the vertex always in the middle. - A polygon is a closed figure made of three or more line segments
that meet only at the vertices. A three-sided polygon is a
triangle, written
△ABC. Four sides is a quadrilateral.
The drawings can look almost the same. What changes is the notation above the letters. Reading the notation is part of the skill, and writing it correctly is the other part.
See it: read each notation
The widget below shows a notation; you pick the diagram that matches. Then flip to the other tab and the diagram comes first; you pick the notation. Both directions drill the same eight notation forms.
Try it
Read the notation. Which diagram does it describe?
Problem 1 of 5
Tap a card. The vertex of an angle is always the middle letter.
A few patterns to notice as you work the widget:
- Bar vs arrow vs double-arrow. The marking above the letters
changes the object.
A̅B̅is finite (segment);AB⃗has one endpoint (ray);AB⃡has none (line). - Vertex in the middle.
∠ABCis the angle at B, not at A. Putting the vertex letter anywhere else names a different angle. - Markings on the diagram carry meaning. A small square at an intersection means perpendicular; matching arrowheads on two lines mean parallel; matching hash marks on two segments mean congruent.
Reading diagram markings
Diagrams encode information using a small set of conventional marks. Authors don't write the words "parallel" or "perpendicular" inside the figure. They use a symbol, and you read it.
The same number of hash marks groups objects together. Two segments each with one tick are congruent to each other. Two other segments each with two ticks are congruent to each other, but not to the first pair. The marking is what carries the relationship; the drawing alone wouldn't tell you which segments are meant to be equal.
Where it shows up in real life
A survey plat for an Alberta quarter-section reads like a geometry exercise. The legal description names the corners (for example, the NE-1/4 of Section 14, Township 22, Range 4, West of the 4th Meridian), and the plat draws the lot boundaries as segments between marked posts. North and south fence lines run parallel (matching arrowheads on the plat); cross-fences meet road allowances at right angles (small squares); and shared fence lines between two quarter-sections appear with matching hash marks so the plat reader knows those are the same surveyed distance.
A surveyor who can't read these markings can't read a plat. A Grade 7 student who can read them can pick up the plat for the family farm or acreage and follow what it says.
Worksheet
These aren't graded. Get them right, get them wrong. The goal is to feel out where the notation lands.
Practice · Not graded
MA.7.GEO.1Practice the idea
01 / 09
Which notation correctly names the line segment from A to B?
Multiple choice: which notation names a line segment from A to B?Show common mistakes
Student says
“Treats segment AB (bar over the letters) and ray AB (arrow over the letters) as the same thing.”
What it reveals
Hasn't internalized the segment/ray distinction. The bar vs arrow in the notation directly mirrors what the diagram looks like: a segment has two endpoint dots and no arrows; a ray has one endpoint dot and one arrowhead. Reading the notation carelessly skips the diagram cue.
Targeted response
In the Symbol Reader, render both. Segment A̅B̅ has visible endpoints at A and B, a finite piece of line. Ray AB⃗ starts at A (endpoint) and extends past B with an arrow that signals 'continues forever in this direction.' Same letters, different marking, different object.
Student says
“Names an angle ∠BAC when the vertex is actually C.”
What it reveals
Forgot the vertex-in-the-middle convention. Often the student writes the letters in the order they read them on the page, top-to-bottom or left-to-right, rather than putting the vertex letter in the middle.
Targeted response
In the Symbol Reader, every valid angle name puts the vertex as the MIDDLE letter. If the vertex is C, valid names are ∠BCA or ∠ACB (or just ∠C if it's the only angle at C). Putting C at the end (∠BAC) names a different angle: the one with vertex A, not C.
Student says
“Doesn't notice the hash marks on a diagram and treats two clearly-congruent segments as if they had no relationship.”
What it reveals
Notation literacy gap: the student isn't reading the implicit information encoded in diagram markings. Diagrams aren't decoration; the marks ARE the data.
Targeted response
Hash marks (single, double, triple) on segments mean those segments are CONGRUENT, the same length. Same number of hash marks groups them together. Before solving any geometry problem, scan the diagram once for these markings and read what each one says about the figure.
Going further
Lesson 21 takes these notations and uses them to investigate the four angles at an intersection. Once you can name what you're looking at, you can start asking what's true about it: opposite angles are congruent, adjacent angles sum to 180°, and so on. None of those relationships make sense without first knowing what an "angle at the intersection" is and how to name it.
In Grade 8, you'll meet transformations (translations, reflections, rotations) that move geometric objects without changing their shape. The notation you learned here is what lets you describe where things start and where they end up.