Geometric terms and notation
Use conventional geometric terms and notation to describe, sketch, and draw points, lines, parallel and perpendicular lines, right angles, regular polygons, and reflectively/rotationally symmetric polygons
What a learner can do afterwards
- Use correct notation for line segments (AB), angles (∠ABC), and parallel lines (AB ∥ CD)
- Sketch a regular hexagon and describe its rotational and reflective symmetry
- Identify and label perpendicular and parallel lines in a given figure using standard symbols
1 · Read
Suppose you must tell a friend how to draw a shape using only words. Geometry has its own shorthand for exactly that: instead of long sentences, you name points, lines, and angles with letters and symbols. Anyone who knows the shorthand can read your notation and draw the exact same shape.
Triangle ABC has three corners, named A, B, and C. Its three sides are the segments AB, BC, and CA. The angle at corner B is written ∠ABC. The middle letter always names the vertex, the exact point where the angle opens.
Some pairs of lines get their own symbols too. Lines that stay the same distance apart and never meet are parallel, written AB ∥ CD. Lines that cross to form a perfect square corner are perpendicular, written AB ⊥ CD.
That square corner is a right angle. In a sketch it gets a small square drawn inside it, not the curved arc you use for every other angle. A reader can then tell at a glance which corner is exactly 90 degrees.
A regular polygon has every side the same length and every angle the same size. A regular hexagon has 6 equal sides, so it folds in half 6 different ways: that is 6 lines of reflective symmetry. Turn it about its centre and it lands looking the same 6 times in one full turn, so its rotational symmetry is order 6.
When you sketch a figure, let the symbols do the talking: a small square for a right angle, matching arrows for parallel lines, and letters in order for every angle and segment. That way anyone can rebuild your drawing without guessing.
Letters name the points, ∠, ∥, and ⊥ describe how lines and angles relate, and a small square always marks a right angle.
More to read
Parallel and perpendicular lines review
Parallel lines run side by side forever without meeting, marked with matching arrow ticks. Perpendicular lines meet at square corners (90 degrees), marked with a small square. One arrow on each of two lines means those two are parallel; the numeral counts matched pairs. Length equality uses a different mark: matching small ticks across segments (two ticks on AB, two on CD) means equal length. Arrows never mean equal and ticks never mean parallel, so read each mark in its own language.
3 Ways to Construct a Line Parallel to a Given Line Through a Given Point
Constructing a parallel through a point copies an angle exactly. Set the compass on the given line, swing arcs, and transfer the same opening to the point: equal corresponding angles force the lines parallel. The rhombus hidden in the arcs guarantees the copy. Labelling matters throughout: name the original line, the point and the new line (AB parallel CD uses matching arrows). A construction is finished only when the marks prove the claim.
Properties of shapes: FAQ
Geometric notation is shorthand: AB names the segment between A and B, angle ABC names the corner at B with arms through A and C, and AB parallel CD claims never-meeting lines. The middle letter of an angle always holds the vertex. Symbols compress sentences: the parallel symbol replaces is parallel to, and tick marks replace is equal in length to. Reading notation aloud (segment AB, angle ABC) turns diagrams into statements you can reason with.
Key ideas: draw polygons with specified attributes
Drawing polygons to specification practises terms in action: draw a hexagon (six sides), mark one pair of parallel sides with arrows, and mark two perpendicular sides with squares. Each mark is a promise the drawing must keep. A regular hexagon adds symmetry promises: six equal sides, six lines of reflective symmetry, and sixth-turn rotational symmetry (every 60 degrees). Sketch, mark, then verify each promise against the drawing.
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2 · Watch
En anglaisTake it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.