Geometrical terms

Revise Geometrical terms for Mathematics D 4024 (O Level) — revision notes, 6 practice questions and instant AI marking.

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Cambridge O Level Mathematics (Syllabus D) 4024

Geometrical terms

The big idea: Geometry questions are written in a fixed vocabulary. If you know exactly what "perpendicular bisector", "reflex", "frustum" or "segment" means, half the question is already decoded before you pick up a pen.

Summary — What This Chapter Covers

Point, vertex, line, plane, parallel, perpendicular, perpendicular bisector, bearing.
Right, acute, obtuse and reflex angles; interior and exterior angles.
Similar, congruent and scale factor (you will not be asked to show that two shapes are congruent).
The names of triangles, special quadrilaterals and polygons, regular and irregular.
The vocabulary of solids and nets: face, surface, edge, vertex; prism, pyramid, cone, sphere, hemisphere, frustum.
The vocabulary of a circle: radius (radii), diameter, chord, tangent, major and minor arc, sector, segment.

1. Points, Lines and Planes

Syllabus 4.1 · Paper 1 & 2

The basic words

Term	Meaning
Point	a position, usually named with a capital letter, e.g. A
Vertex (plural vertices)	a corner, where two or more lines or edges meet
Line	a straight line goes on for ever in both directions; the line segment AB has end points A and B
Plane	a flat surface, such as a face of a cuboid or the ground
Parallel	always the same distance apart and never meet (marked with matching arrows)
Perpendicular	meet at a right angle (90°)
Perpendicular bisector of AB	the line through the midpoint of AB at right angles to AB
Bearing	a direction measured clockwise from north, written with three figures, e.g. 065°

Worked Example

The points P(1, 2), Q(7, 2) and R(7, 6) are plotted on a grid. (a) Which two of the line segments PQ, QR and PR are perpendicular? (b) Write down the coordinates of the point where the perpendicular bisector of PQ crosses PQ.

2. Types of Angle

Syllabus 4.1 · Paper 1 & 2

Acute, right, obtuse, reflex; interior and exterior

Name	Size
Acute	more than 0° and less than 90°
Right angle	exactly 90° (marked with a small square)
Obtuse	more than 90° and less than 180°
Reflex	more than 180° and less than 360°

An interior angle of a polygon is inside the shape, between two sides. An exterior angle is between one side and the next side extended outwards. At each vertex, interior angle + exterior angle = 180°.

Angles are named with three letters, the vertex in the middle: angle ABC is the angle at B between BA and BC.

Practice Question 1

(a) Write down the type of each angle: 172°, 90°, 236°, 47°. (b) The obtuse angle at a point is 140°. Work out the reflex angle at the same point.

3. Similar, Congruent and Scale Factor

Syllabus 4.1 · Paper 1 & 2

Same shape, same size

Congruent shapes are identical: same shape and same size (one may be a reflection or rotation of the other). Similar shapes have the same shape but may be a different size: all angles are equal and all lengths are in the same ratio. The scale factor is that ratio: new length ÷ original length.

Scale factor scale factor = length on the new shape ÷ matching length on the original shape

Worked Example

Congruent is just a word here

4. Triangles and Special Quadrilaterals

Syllabus 4.1 · Paper 1 & 2

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Also in the full note

The names and what they promise
Regular and irregular
Faces, surfaces, edges and vertices
Twelve words to know exactly

What's inside

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Geometrical terms