IGCSE · Practice questions · Geometrical terms: shapes, solids and nets

The words of geometry.

Six original Cambridge-style questions on geometrical terms: angle types, special quadrilaterals, solids, nets and the vocabulary of a circle.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Name it by what it must have.

Angles: acute below 90°, obtuse 90° to 180°, reflex 180° to 360°.
Quadrilaterals: check parallel sides, equal sides, right angles and diagonals in turn.
Solids: count faces, then edges, then vertices; check \(F + V - E = 2\).
Circles: sector = two radii and an arc; segment = chord and arc.
Use the exact word: the mark is for the correct term, spelt clearly.

Recall

[2 marks]

Write down the type of each angle: (a) \(89^\circ\) (b) \(91^\circ\) (c) \(181^\circ\) (d) \(90^\circ\).

(a) acute (b) obtuse (c) reflex (d) right angle ✓

Recall

[2 marks]

Name the quadrilateral:

(a) two pairs of equal adjacent sides, and diagonals that cross at right angles but are not equal and do not both get bisected;

(b) opposite sides equal and parallel, four right angles, and two different side lengths.

(a) kite ✓
(b) rectangle ✓

Recall

[3 marks]

Write down the word for:

(a) a straight line that touches a circle at exactly one point;

(b) a chord that passes through the centre;

(a) tangent ✓
(b) diameter ✓
(c) sector ✓

Calculation

[3 marks]

A pyramid has a hexagon as its base. Find the number of (a) faces (b) edges (c) vertices.

(a) 1 hexagon + 6 triangles = 7 faces. ✓
(b) 6 base edges + 6 slant edges = 12 edges. ✓
(c) 6 base vertices + 1 apex = 7 vertices. ✓
Check: \(7 + 7 - 12 = 2\). ✓

Analysis

[3 marks]

The hands of a clock show exactly 8 o'clock.

(a) Find the obtuse angle between the hands.

(b) Find the reflex angle between the hands.

(a) Each hour gap is \(30^\circ\). From 8 round to 12 is 4 gaps: \(4 \times 30 = 120^\circ\). ✓
(b) \(360 - 120 = 240^\circ\). ✓
(c) The hour hand must be 4 gaps from 12 on the other side: 4 o'clock. ✓

Analysis

[4 marks]

A flower bed PQRS is a quadrilateral. PQ is parallel to SR, PQ = 6 m, SR = 10 m and PS = QR = 5 m.

(a) Name the shape PQRS.

(b) Explain why PQRS is not a parallelogram.

(d) Diagonal PR splits the bed into two triangles. Are these triangles congruent? Explain.

(a) Exactly one pair of parallel sides: a trapezium (an isosceles trapezium, since PS = QR). ✓
(b) In a parallelogram both pairs of opposite sides are equal, but PQ = 6 m and SR = 10 m are not equal. ✓
(c) SR is the longer parallel side, so S and R are the base corners and PS slopes inwards: the horizontal step is \((10 - 6) \div 2 = 2\) m, so angle PSR is acute (its co-interior partner SPQ is obtuse). ✓
(d) No. Triangle PQR has sides 6, 5 and PR, but triangle PSR has sides 5, 10 and PR. They share PR but the other sides differ, so they are not identical. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.