Geometrical Terms
The words of geometry — angles, shapes, circles and solids
Geometry questions are full of special words. If you know exactly what each word means, many marks become easy. Learn this page like vocabulary.
Points and lines. A point marks a position. A vertex (plural vertices) is a corner where lines meet. Parallel lines are always the same distance apart and never meet (marked with matching arrows). Perpendicular lines meet at a right angle (90°).
Angles.
- Acute — less than 90°.
- Right angle — exactly 90° (marked with a small square).
- Obtuse — between 90° and 180°.
- Straight line — exactly 180°.
- Reflex — between 180° and 360°.
Triangles. Equilateral: 3 equal sides, 3 equal angles (each 60°). Isosceles: 2 equal sides and 2 equal angles. Scalene: no equal sides, no equal angles. Right-angled: one angle is 90°.
Quadrilaterals (4 sides):
- Square — 4 equal sides, 4 right angles, 2 pairs of parallel sides.
- Rectangle — 4 right angles, opposite sides equal and parallel.
- Rhombus — 4 equal sides, opposite sides parallel, opposite angles equal (a “pushed-over square”).
- Parallelogram — opposite sides equal and parallel, opposite angles equal.
- Trapezium — exactly one pair of parallel sides.
- Kite — two pairs of equal sides next to each other (adjacent), one pair of equal opposite angles.
Polygons are flat shapes with straight sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10). A regular polygon has all sides equal and all angles equal.
Parts of a circle — study the diagram:
- Centre O; radius — centre to the edge; diameter — edge to edge through the centre (diameter = 2 × radius); circumference — the distance all the way round.
- Chord — a straight line joining two points on the circle (a diameter is the longest chord). Tangent — a straight line that touches the circle at exactly one point.
- Arc — part of the circumference. Sector — a “pizza slice” between two radii and an arc. Segment — the region between a chord and an arc. A semicircle is half a circle.
Solids (3-D shapes). Cube and cuboid (6 flat faces), prism (the same cross-section all the way through, for example a triangular prism), cylinder, pyramid (a base with triangular faces meeting at a point), cone, sphere and hemisphere (half a sphere). A face is a surface, an edge is where two faces meet, and a vertex is a corner. A net is the flat shape you fold up to make a solid.
Name the type of each angle: (a) 35° (b) 90° (c) 140° (d) 210°
(a) Less than 90° → acute. (b) Exactly 90° → right angle.
(c) Between 90° and 180° → obtuse. (d) Between 180° and 360° → reflex.
A quadrilateral has four equal sides, but its angles are not right angles. Its opposite sides are parallel. Name it.
Four equal sides means square or rhombus. No right angles rules out the square. It is a rhombus.
Tip: work through the list of properties and cross shapes out — exactly like a detective.
A circle has radius 6 cm. (a) What is the length of its diameter? (b) A line touches the circle at one point only. What is it called? (c) What is the region between a chord and the arc called?
(a) Diameter = 2 × radius = 2 × 6 = 12 cm.
(b) A tangent. (c) A segment (not a sector — a sector is bounded by two radii).
A chocolate box is a triangular prism. How many faces, edges and vertices does it have? What does its net look like?
Faces: 2 triangles (the ends) + 3 rectangles = 5 faces.
Edges: 3 on each triangle (6) + 3 joining the triangles = 9 edges.
Vertices: 3 on each triangle = 6 vertices.
Its net is 3 rectangles in a row with a triangle attached to each side of the middle rectangle. Check with Euler’s rule: faces + vertices − edges = 5 + 6 − 9 = 2 ✔ (this works for every solid with flat faces).
Q1. Write down the type of each angle: (a) 72° (b) 250° (c) 135° (d) 90°
👀 Show answer
(B1 for 2 or 3 correct)
Q2. Name the type of triangle:
(a) angles 70°, 70° and 40° (b) sides 5 cm, 7 cm and 9 cm (c) angles 60°, 60° and 60°
👀 Show answer
(b) scalene ✓ B1
(c) equilateral ✓ B1
Q3. Name each quadrilateral.
(a) It has exactly one pair of parallel sides.
(b) It has two pairs of equal adjacent sides and one pair of equal opposite angles.
(c) It has four right angles, but its sides are not all equal.
👀 Show answer
(b) kite ✓ B1
(c) rectangle ✓ B1
Q4. Write down the name of a polygon with: (a) 5 sides (b) 6 sides (c) 8 sides (d) 10 sides
👀 Show answer
(B1 for 2 or 3 correct)
Q5. The diagram shows a circle with centre O. Name the parts labelled A, B, C, D, E, F and G. (A, B, C and D are lines; E and F are shaded regions; G is the thick curved part.)
👀 Show answer
E sector F segment G arc ✓ B3
(B2 for 5 or 6 correct, B1 for 3 or 4 correct)
Q6. The diagram shows four right-angled triangles.
(a) Which triangle is congruent to triangle A? (b) Which triangle is similar to triangle A but not congruent to it?
👀 Show answer
(b) B ✓ B1
Q7. Complete the table.
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cuboid | |||
| Square-based pyramid | |||
| Cone |
👀 Show answer
Square-based pyramid: 5 faces, 8 edges, 5 vertices ✓ B1
Cone: 2 faces (1 flat, 1 curved), 1 edge, 1 vertex ✓ B1
Q8. Name the solid made by folding each net.
(a) Six identical squares. (b) Two circles and a rectangle. (c) One square and four identical triangles.
👀 Show answer
(b) cylinder ✓ B1
(c) square-based pyramid ✓ B1
Q9. ABCD is a rectangle, with the vertices in order around it. (a) Name the side that is parallel to AB. (b) Name a side that is perpendicular to AB.
👀 Show answer
(b) BC or AD ✓ B1
- Mixing up sector and segment: a sector has two radii (a pizza slice); a segment is cut off by a chord.
- Mixing up chord and tangent: a chord crosses the circle (two points); a tangent only touches it (one point).
- Calling a reflex angle obtuse: obtuse stops at 180°. Anything between 180° and 360° is reflex.
- Kite versus parallelogram: a kite’s equal sides are next to each other; a parallelogram’s equal sides are opposite.
- Congruent versus similar: congruent means the same size too; similar shapes can be bigger or smaller.
- Forgetting curved faces: a cylinder has 3 faces (2 flat, 1 curved), 2 edges and 0 vertices.
- Paper 1 and Paper 3 often start a geometry question with “Write down the mathematical name of…” or “Name the type of angle…” — 1 mark each.
- Circle words (chord, tangent, sector, segment) are tested on a labelled diagram and come back in angle and area questions later in the course.
- Command words: write down, name, complete the table, which shape is….
- Spelling matters only if the word is unclear — but write clearly: “isosceles”, “parallelogram”, “trapezium”.
(then move on to the next unit in the Geometry strand)