IGCSE Maths · Geometry · Core & Extended

Geometrical Terms and Vocabulary: The Language of Shape

This is the vocabulary every later Geometry note assumes you already know — angle types, triangle and quadrilateral names, polygon and solid terms, and circle parts. Almost all of it is shared between Core and Extended; a small handful of extra terms are Extended-only, tagged below.

1. Points, Lines and Angle Types

Point — an exact position, no size
Vertex (plural vertices) — a corner, where two lines meet
Line — a straight path extending infinitely in both directions
Plane — a flat surface extending infinitely in two dimensions Ext.
Angle types Acute (<90°) Right (90°) Obtuse (90–180°) Reflex (>180°)
Try it — Angle Types
  1. Classify a 35° angle.
  2. Classify a 150° angle.
  3. Classify a 210° angle.
  4. What type of angle is exactly 90°?
Show answers
  1. Acute
  2. Obtuse
  3. Reflex
  4. Right angle

2. Parallel and Perpendicular Lines, Bearings

Parallel — lines that never meet, always the same distance apart
Perpendicular — lines that meet at a right angle
Perpendicular bisector — a line that crosses another at 90°, exactly at its midpoint Ext.
Bearing — a direction measured clockwise from north, given as three digits (e.g. 065°)
Interior angle — an angle inside a shape, between two adjacent sides
Exterior angle — the angle between a side and the extension of the adjacent side
Similar — same shape, angles match, sides in the same ratio, but not necessarily the same size
Congruent — exactly the same shape and size

3. Triangles

The four types of triangle Equilateral Isosceles Scalene Right-angled Equilateral: all 3 sides equal, all angles 60°. Isosceles: exactly 2 sides equal, 2 angles equal. Scalene: no sides equal, no angles equal. Right-angled: one angle is exactly 90°.
Try it — Triangles
  1. A triangle has sides 5 cm, 5 cm, and 8 cm. What type is it?
  2. A triangle has angles 60°, 60°, and 60°. What type is it?
  3. A triangle has sides 3 cm, 4 cm, and 5 cm, with a 90° angle. What type(s) apply?
Show answers
  1. Isosceles (two equal sides)
  2. Equilateral
  3. Scalene and right-angled (no two sides equal, but it does have a right angle — a triangle can belong to more than one category)

4. Special Quadrilaterals

Six special quadrilaterals Square Rectangle Rhombus Parallelogram Kite Trapezium Square: 4 equal sides, 4 right angles. Rectangle: opposite sides equal, 4 right angles. Rhombus: 4 equal sides, opposite angles equal (a “squashed square”). Parallelogram: opposite sides equal and parallel. Kite: two pairs of adjacent equal sides. Trapezium: exactly one pair of parallel sides.
Try it — Quadrilaterals
  1. Name a quadrilateral with 4 equal sides but no right angles.
  2. Name a quadrilateral with exactly one pair of parallel sides.
  3. What’s the key difference between a rectangle and a square?
Show answers
  1. Rhombus
  2. Trapezium
  3. A square has all 4 sides equal; a rectangle only needs opposite sides equal (a square is technically a special rectangle).

5. Polygons

Sides5678910
NamePentagonHexagonHeptagonOctagonNonagonDecagon

A regular polygon has all sides and all angles equal; an irregular polygon doesn’t.

Try it — Polygons
  1. Name the polygon with 8 sides.
  2. Name the polygon with 6 sides.
  3. Is a regular polygon always convex-looking with equal sides and angles, or can the sides differ in length?
Show answers
  1. Octagon
  2. Hexagon
  3. All sides and all angles must be equal for a polygon to be called regular.

6. Solids and Nets

Cube — 6 equal square faces
Cuboid — 6 rectangular faces
Prism — same cross-section all along its length
Cylinder — a prism with a circular cross-section
Pyramid — a base with triangular faces meeting at a point (apex)
Cone — a circular base narrowing to a point
Sphere — a perfectly round 3D shape
Hemisphere — exactly half a sphere Ext.
Frustum — a cone or pyramid with its top sliced off Ext.
Net — a 2D shape that folds up into a 3D solid
Face — a flat (or curved) surface of a solid
Edge — where two faces meet
Try it — Solids
  1. How many faces does a cube have?
  2. What solid has a circular base and comes to a single point?
  3. What is the term for exactly half a sphere? Ext.
Show answers
  1. 6
  2. Cone
  3. Hemisphere

7. Circle Vocabulary

Parts of a circle centre radius diameter chord tangent arc
Radius (plural radii) — from the centre to the edge
Diameter — right across through the centre; 2 × radius
Circumference — the distance all the way around
Semicircle — exactly half a circle
Chord — a straight line joining two points on the circumference
Tangent — a line that touches the circle at exactly one point
Arc — part of the circumference (major/minor arc distinguishes the longer/shorter one) Ext.
Sector — a “pizza slice” area, bounded by two radii and an arc
Segment — the area between a chord and the arc it cuts off
Try it — Circle Vocabulary
  1. What’s the difference between a chord and a diameter?
  2. What word describes a line that touches a circle at exactly one point?
  3. What’s the difference between a sector and a segment?
Show answers
  1. A diameter is a chord that passes through the centre; a chord in general doesn’t have to.
  2. Tangent
  3. A sector is bounded by two radii and an arc (like a pizza slice); a segment is bounded by a chord and an arc (a “cut off” piece, not through the centre).
Common mistakes to watch for
  • Mixing up “similar” (same shape, different size) with “congruent” (identical in shape and size) — these mean different things in exams.
  • Confusing a chord with a tangent — a chord has both endpoints on the circle; a tangent only touches at one point and extends beyond it.
  • Assuming all four-sided shapes with two pairs of parallel sides are the same — check carefully whether it’s specifically a square, rectangle, rhombus, or general parallelogram.
  • Miscounting a polygon’s sides when naming it — always count carefully, especially for pentagon vs hexagon.
  • Mixing up sector and segment — remember “sector” sounds like a slice from the centre; “segment” is cut off by a straight chord.

8. Quick-Fire Challenge Round

True or False?
  1. A reflex angle is always bigger than 180°.
  2. A rhombus is always a square.
  3. Congruent shapes must be exactly the same size.
  4. A cylinder is a type of prism.
Show answers
  1. True.
  2. False — a rhombus has 4 equal sides but doesn’t need right angles; a square is a special rhombus, but not every rhombus is a square.
  3. True — congruent means identical in both shape and size, unlike similar.
  4. True — it has a constant (circular) cross-section throughout its length.
Spot the Error
  1. “A shape with 4 equal sides must be a square.”
  2. “An obtuse angle is between 0° and 90°.”
  3. “A tangent to a circle crosses through the circle’s interior.”
Show answers
  1. Not necessarily — a rhombus also has 4 equal sides but doesn’t need right angles.
  2. That’s the range for an acute angle; obtuse is between 90° and 180°.
  3. A tangent touches the circle at exactly one point and stays outside — it never crosses into the interior.

9. Mixed Practice — Bringing It All Together

  1. Classify a 100° angle.
  2. Name a triangle with all sides different lengths.
  3. Name the quadrilateral with two pairs of adjacent equal sides.
  4. Name the 9-sided polygon.
  5. What is the line from the centre of a circle to its edge called?
Show answers
  1. Obtuse
  2. Scalene
  3. Kite
  4. Nonagon
  5. Radius

Practice at Home

A large set again — take it steadily.

Part A — Angles and lines
  1. Classify: 15°, 95°, 300°, 90°.
  2. What term describes two lines that never meet?
  3. What term describes two lines meeting at a right angle?
Part B — Triangles and quadrilaterals
  1. A triangle has sides 6 cm, 8 cm, and 10 cm, with one 90° angle. Name every category it belongs to.
  2. Name a quadrilateral with opposite sides parallel but no right angles and unequal side lengths.
  3. Explain, in your own words, the difference between a kite and a rhombus.
Part C — Polygons and solids
  1. Name the polygon with 7 sides.
  2. Name a solid with a triangular or square base and faces meeting at a single apex.
  3. What is the term for a pyramid or cone with its top cut off? Ext.
Part D — Circle vocabulary
  1. Name the region bounded by two radii and an arc.
  2. Name the region bounded by a chord and an arc.
  3. What is exactly half of a circle called?
Part E — Applied / challenge
  1. Sketch (in words) a shape that is both a rectangle and a rhombus. What special name does this shape have?
  2. Explain why every square is a rectangle, but not every rectangle is a square.
  3. A student says “all circles’ diameters are chords, but not all chords are diameters.” Explain whether this statement is correct.

Key Vocabulary Recap

Congruent — identical shape and size
Similar — same shape, proportional sides, possibly different size
Regular polygon — all sides and angles equal
Net — a 2D shape that folds into a 3D solid
Tangent — touches a circle at exactly one point
Sector / segment — a “slice” (via two radii) vs a “cut-off piece” (via a chord) of a circle

Syllabus Reference

This note covers Cambridge IGCSE Mathematics (0580) section C4.1 (Core subject content) and section E4.1 (Extended subject content) — Geometrical terms. Almost all vocabulary is shared between tiers; the small Extended-only additions (plane, perpendicular bisector as a named term, hemisphere, frustum, and the major/minor arc distinction) are marked above. Neither tier requires candidates to formally prove congruence.

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