This mini-lesson covers the Geometry & Measures strand of Edexcel GCSE Maths (1MA1): angle rules, polygons, Pythagoras, trigonometry (SOHCAHTOA), area & volume, circle theorems, transformations, vectors and bearings.
Work through each screen, answer the questions as you go (some are wordy, most are calculations) and collect ⭐ stars. Press Start when you're ready.
The basic angle rules are the backbone of every geometry question. Learn these three facts:
Two angles on a straight line are 130° and x.
They add to 180°: x = 180 − 130
x = 50°
Common slip: mixing up the totals. A straight line is 180°, a full turn around a point is 360°. Don't use 360° when the angles only sit on a line.
Split any polygon into triangles from one corner. An n-sided polygon splits into (n − 2) triangles, each 180°:
The exterior angles of ANY polygon add to 360°.
For a regular hexagon: exterior angle = 360 ÷ 6 = 60°
Check: interior + exterior = 120 + 60 = 180° ✓
Remember: exterior angles always sum to 360° (a full turn), so for a regular polygon each exterior angle = 360 ÷ n. Interior and its exterior angle are on a straight line, adding to 180°.
In a right-angled triangle, the square on the longest side (the hypotenuse) equals the sum of the squares on the other two:
Right triangle with legs 6 and 8. Find the hypotenuse.
c² = 6² + 8² = 36 + 64 = 100
c = √100 = 10
Watch out: to find a shorter side you subtract: a² = c² − b². Only use + when the hypotenuse is the unknown.
Walk once around any polygon and you make a full 360° turn. The exterior angles are those turns, so they always add to 360°:
A regular hexagon has 6 sides.
Exterior angle = 360 ÷ 6 = 60°
So each interior angle = 180 − 60 = 120° ✓
Handy check: for a regular polygon, number of sides n = 360 ÷ (exterior angle). If someone gives you an exterior angle of 40°, then n = 360 ÷ 40 = 9 sides.
Area formulas turn measurements into a region. The circle's area uses the radius squared:
Find the area of a circle with radius 5, as a multiple of π.
area = π r² = π × 5² = π × 25
= 25π
Common slip: squaring the diameter, or forgetting to square at all. It is π × r × r — square the radius, not the diameter, and not "2 × r".
A prism has the same cross-section all the way through. Its volume is the cross-section area times the length:
A cuboid measures 2 cm × 3 cm × 4 cm.
volume = 2 × 3 × 4 = 24 cm³
A cylinder has radius 3 cm and height 10 cm.
volume = π r² h = π × 3² × 10 = 90π cm³
Units: volume is always cubic (cm³, m³). If you multiply three lengths you must get a cubed unit — a quick check that your working makes sense.
In a right-angled triangle, the three ratios link an angle to two sides. Label sides relative to the angle θ: opposite, adjacent, hypotenuse.
A right triangle has hypotenuse 10 and an angle of 30°. Find the side opposite the 30°.
Use SOH: sin 30° = opp ÷ hyp, so opp = hyp × sin 30°
opp = 10 × 0.5 = 5
Trap: pick the ratio that uses the two sides you know/want. If you have the hypotenuse and want the opposite, that's sin — not tan.
Tap a regular polygon on the left, then its matching interior angle on the right.
Circle theorems are angle rules linked to a circle. A few of the key ones:
The angle at the centre subtended by an arc is 100°.
Angle at the circumference (same arc) = half of that
= 100 ÷ 2 = 50°
Exam tip: always state the theorem you used ("angle at centre = 2 × angle at circumference"). Marks are given for the reason, not just the number.
A transformation moves or resizes a shape. There are four to know, each needing specific information to describe fully:
Fully describe: each transformation needs the right details. A rotation without a centre, or an enlargement without a scale factor, loses marks even if the picture looks right.
A vector has magnitude and direction, written as a column: the top number is movement right, the bottom is movement up. Add vectors by adding their components:
Magnitude: the length of a vector (x over y) is √(x² + y²) — Pythagoras again. Direction and length together define the vector.
A bearing is a direction measured clockwise from North, always written with three digits (e.g. 045°, 210°).
Three-figure rule: a bearing of 45° must be written as 045°. Back-bearings differ by 180° (add or subtract 180 to reverse direction).
An acute angle is less than 90°; an obtuse angle is between 90° and 180°. Tap an angle, then tap the box it belongs in.
Angles: line = 180°, point = 360°, triangle = 180°.
Polygons: interior sum = (n − 2) × 180°; exterior angles sum to 360°, so each = 360 ÷ n.
Pythagoras: a² + b² = c² in right-angled triangles (subtract to find a shorter side).
Trigonometry: SOH CAH TOA — sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
Area & volume: circle area = πr²; prism/cylinder volume = cross-section × length.
Circle theorems: semicircle = 90°, centre = 2 × circumference, cyclic quad opposite = 180°.
Transformations: translation, reflection, rotation, enlargement — describe each fully.
Vectors & bearings: column vectors add componentwise; bearings are 3-figure, clockwise from North.
You've covered the Geometry & Measures strand of Edexcel 1MA1 — angle rules through to vectors and bearings. Press Finish to see your score.
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