Angles on lines & around points

The three angle facts you use most often:

Common slip: mixing up 180° (on a straight line) with 360° (all the way around a point). Draw the diagram and check which rule the angles sit on.

Your turn — angles on a line

Parallel lines & around a point

When a straight line crosses parallel lines, equal angles appear in a pattern:

• Corresponding angles (an "F" shape) are equal.
• Alternate angles (a "Z" shape) are equal.
• Co-interior angles (a "C" shape) add to 180°.

Watch out: these rules only work when the lines are parallel (shown by matching arrows). Without the arrows you can't assume the angles are equal.

Your turn — angles around a point

Interior & exterior angles

For any polygon with n sides:

Key fact: the exterior angles of any polygon always add to 360°. For a regular polygon just divide 360 by the number of sides.

Exterior angle of a hexagon

Your turn — interior angle sum

Pythagoras' theorem

In a right-angled triangle, the square on the longest side (the hypotenuse) equals the sum of the squares on the other two sides:

Common slip: to find a shorter side you subtract (c² − a²), not add. Only add when you're hunting the hypotenuse.

Your turn — find the hypotenuse

Trigonometry — SOHCAHTOA

In a right-angled triangle the three trig ratios link an angle θ to the sides opposite, adjacent and hypotenuse:

Learn the exact values: sin 30° = 0.5, cos 60° = 0.5, tan 45° = 1. These are worth memorising for non-calculator marks.

Your turn — trigonometry

Area & volume formulae

Area is measured in square units (cm²); volume in cubic units (cm³). The most-used formulae:

Watch the height: for a triangle use the perpendicular height (straight up from the base), not a slanted side.

Area of a triangle

Your turn — volume of a cuboid

Setup ⇄ formula

Tap a shape or ratio on the left, then its matching formula on the right.

Transformations

Four ways to move a shape on a grid. Only one changes the shape's size:

• Translation — slide it; describe with a column vector.
• Reflection — flip it in a mirror line.
• Rotation — turn it about a centre (angle + direction).
• Enlargement — resize by a scale factor from a centre.

Remember: translation, reflection and rotation all produce a congruent image. An enlargement produces a similar shape (same angles, scaled lengths).

Bearings

A bearing is a direction measured clockwise from North, always written with three figures (e.g. 070°, not 70°).

Three figures always: write a bearing of 70 degrees as 070°. A missing leading zero loses marks in exams.

Back bearing

Circle theorems (Higher tier)

The circle theorems relate angles made by chords, radii and tangents. Three you meet most:

• Angle at the centre = twice the angle at the circumference (same arc).
• Angle in a semicircle is 90°.
• A tangent meets a radius at 90°.

Higher only: circle theorems are on the Higher tier of J560. Always state the theorem you used to earn the reasoning mark.

Vectors (Higher tier)

A vector has both size and direction, written as a column vector — top number is movement across, bottom is up/down:

Higher only: vector geometry (and proofs using vectors) sits on the Higher tier. A negative vector reverses the direction, e.g. −(3 over 2) = (−3 over −2).

Acute or obtuse?

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.

The whole Geometry & Measures strand

You've covered the Geometry & Measures strand of OCR GCSE Maths (J560) — Foundation content plus the Higher-tier circle theorems and vectors. Press Finish to see your score.