Equilateral triangle
Three equal sides; three angles of 60°.
CAMBRIDGE O LEVEL · 2025–2027
Geometrical terms.
Name shapes, angles, solids and circle features precisely, so every diagram has a clear meaning.
BY THE END
Use geometrical terms · classify triangles, quadrilaterals, polygons and solids · recognise circle vocabulary
01
The language of position and angle
Geometry begins with descriptions of position and direction. A point marks a location, a line continues indefinitely, and a line segment has two endpoints. A ray has one endpoint and continues in one direction.
An angle measures the turn between two rays meeting at a vertex. Learn these basic objects before learning the names of more elaborate shapes, because constructions and proofs use the same words precisely rather than as visual guesses.
Use the precise word for the feature in the diagram. A diagram supports a statement; a geometrical property explains why it is true.
Point
An exact position, with no size. A vertex is a corner where edges or sides meet.
Line and plane
A line extends indefinitely in both directions. A line segment has two endpoints. A plane is a flat two-dimensional surface extending indefinitely.
Parallel
Lines in the same plane that never meet.
Perpendicular
Lines meeting at a right angle, 90°.
Perpendicular bisector
A line at 90° to a segment through its midpoint.
Bearing
A clockwise angle from north, written using three figures, such as 025°.
Interior and exterior
An interior angle is inside a polygon. The usual exterior angle lies between a side and the extension of an adjacent side.
Similar and congruent
Similar shapes have the same shape: corresponding angles equal and corresponding lengths in a constant ratio. Congruent shapes have the same shape and size.
Scale factor
The multiplier taking corresponding lengths from the original shape to the image. A length scale factor compares positive lengths.
Acute: 0° < θ < 90°Right: 90°Obtuse: 90° < θ < 180°Reflex: 180° < θ < 360°
A straight angle is 180° and a complete turn is 360°.
Pause and explainWhat is the difference between a line and a segment?
A segment has two fixed endpoints. A line continues without end in both directions.
02
Triangles, quadrilaterals and polygons
A plane shape is flat and two-dimensional. Its sides and angles determine its properties. The name of a shape may tell us about its number of sides, equal lengths or parallel sides.
Do not judge a shape only by its orientation on the page. A tilted square remains a square. Look for markings and definitions: equal-length ticks, parallel arrows and right-angle boxes communicate facts that a drawing’s appearance alone cannot establish.
Isosceles triangle
Two equal sides; opposite base angles equal.
Scalene triangle
All three side lengths different.
Right-angled triangle
One angle is exactly 90°; classification by angle can overlap a side classification.
Square
Four equal sides; four right angles.
Rectangle
Opposite sides equal and parallel; four right angles.
Rhombus
Four equal sides; opposite sides parallel and opposite angles equal.
Parallelogram
Opposite sides equal and parallel; opposite angles equal.
Kite
Two pairs of adjacent equal sides.
Trapezium
A pair of opposite parallel sides. In the usual school classification, one pair only.
Pentagon: 5 sidesHexagon: 6Octagon: 8Decagon: 10
A polygon is a closed plane figure made from straight sides. A circle is not a polygon.
WORKED EXAMPLE
Classify triangles with sides 5, 5, 6 and 10, 10, 12.
Both triangles are isosceles because each has two equal sides. Their corresponding lengths have scale factor 2, so the triangles are similar. They are not congruent because they have different sizes.
Pause and explainDoes rotating a rectangle change its right angles?
No. Its orientation changes, but the side lengths and angles that define the shape stay the same.
03
Solids, surfaces and nets
A solid occupies three-dimensional space. A face is a surface, an edge is where surfaces meet, and a vertex is a corner. A net lays out the surfaces so the solid can be folded from a flat sheet.
Connect the flat net with the assembled object. Count a shared edge once on the solid rather than once for each touching face, and distinguish curved surfaces from flat faces where the question requires it. Visualise which edges meet when folding.
A face is a flat surface of a solid. Solids can also have curved surfaces. An edge is where faces meet; for curved solids, questions may also refer to circular edges where surfaces meet. A net unfolds a solid’s surface into a plane.
Cube
Six congruent square faces, 12 edges, 8 vertices.
Cuboid
Six rectangular faces; 12 edges and 8 vertices. All cube edges are equal; a general cuboid has three edge lengths.
Prism
A uniform cross-section along its length, with two congruent parallel polygonal ends.
Cylinder
Two parallel circular flat surfaces and one curved surface.
Pyramid
A polygonal base and triangular side faces meeting at an apex.
Cone
A circular base and a curved surface meeting at an apex.
Sphere
A curved surface whose points are all the same distance from its centre.
Hemisphere
Half a sphere, with one circular flat surface.
Frustum
The portion left after cutting a cone or pyramid parallel to its base and removing the smaller top portion.
Pause and explainWhy must a cube net contain six squares?
A cube has six square faces. The net must provide one face for each, arranged so they can fold without overlap.
04
Name each part of a circle
A circle is the collection of points at a fixed distance from its centre. That fixed distance is the radius. A diameter runs through the centre from one side of the circle to the other.
Other circle terms describe different parts: a chord joins two circumference points, an arc is part of the circumference, a sector is a wedge bounded by radii, and a segment is cut off by a chord. Distinguish the boundary lines from the enclosed regions.
The circumference is the circle’s boundary, or its total length in a measurement question. A semicircle is half a circle, divided by a diameter. The centre is equally distant from every point on the circumference.
A radius joins the centre to the circumference. A diameter is a chord through the centre and is twice the radius.
Pause and explainIs every chord a diameter?
No. A diameter is the special chord that passes through the centre.
05
Your turn. Use the exact term.
Read each term as a definition and identify the relevant feature in a sketch. Use markings to support claims about equality, parallelism or right angles.
When a shape looks unfamiliar, rotate it mentally rather than changing its classification. For solids, use a net or simple sketch to keep faces, edges and vertices distinct.
1
Name an angle of 135° and an angle of 250°.
Reveal worked answer
135° is obtuse. 250° is reflex. Neither is acute or right-angled.
2
A quadrilateral has four equal sides but no right angles. Name it. Is it necessarily regular?
Reveal worked answer
It is a rhombus. It is not regular: a regular quadrilateral must also have equal angles, making it a square.
3
What distinguishes a sector from a segment of a circle?
Reveal worked answer
A sector is bounded by two radii and an arc. A segment is bounded by a chord and an arc.
4
A solid has a uniform pentagonal cross-section along its length. Name it and state the shape of its two ends.
Reveal worked answer
A pentagonal prism, with two congruent parallel pentagonal ends.