Geometry
Pythagoras, angles, and area.
Learn
Geometry, explained point by point
Everything the GCSE specification expects you to be able to do, and how to actually do it - the same lesson a signed-in student studies from.
Use angle facts: angles on a straight line, around a point, and vertically opposite angles
Angles on a straight line add to 180°, angles around a point add to 360°, and when two lines cross, opposite angles are equal. In written answers, quote the fact you used - "angles on a straight line sum to 180°" - because the reason carries marks.
Use the angle sums of triangles and quadrilaterals
A triangle's angles sum to 180° and a quadrilateral's to 360°. Special triangles give more for free: isosceles means two equal base angles, so a 40° apex leaves (180 − 40) ÷ 2 = 70° for each. Mark equal sides and angles on the diagram as you go.
Use alternate, corresponding and co-interior angles with parallel lines
A line crossing parallel lines makes alternate angles ("Z-angles") equal, corresponding angles ("F-angles") equal, and co-interior angles ("C-angles") summing to 180°. Use the proper names in your reasons - "Z-angles" alone does not earn the mark.
Find interior and exterior angles of polygons
Exterior angles of ANY polygon add to 360°, so a regular decagon's exterior angle is 36° and its interior angle is 180 − 36 = 144°. For interior sums, (n − 2) × 180° - a pentagon holds 540°. The exterior-angle route is usually the fastest for regular shapes.
Calculate areas of triangles, rectangles, parallelograms and trapezia
Triangle: ½ × base × height. Parallelogram: base × height. Trapezium: ½(a + b)h - average the parallel sides, times the height. In every formula the height is the PERPENDICULAR height, not a slanted side.
Find perimeters and areas of compound shapes
Split the shape into rectangles and triangles, find any missing sides by adding and subtracting the ones given, then total the areas. For perimeter, trace the outline once - inside dividing lines never count.
Practice
Try a Geometry question
A GCSE-style original question from this topic. Have a go before you open the working - deciding on an answer first is what makes the working stick.
A circular table top has a diameter of 14 cm. Work out its area. Give your answer in terms of π.
- 196π cm²
- 49π cm²
- 14π cm²
- 28π cm²
Show the answer and the working
Answer: 49π cm²
Area = πr². Halve the diameter first: r = 7 cm, so the area is 49π cm².
- The area formula is A = πr², which needs the radius.
- The radius is half the diameter: 14 ÷ 2 = 7 cm.
- Substitute: A = π × 7² = 49π.
- The area is 49π cm².