Geometry
What the exam tests
Geometry tests angle types and angle facts, properties of triangles and quadrilaterals, circles, symmetry and simple 2D and 3D shapes.
Core rules
- Acute angles are less than 90°, right angles are exactly 90°, obtuse angles are between 90° and 180°, and a straight angle is 180°.
- The angles in a triangle add to 180°. The angles in a quadrilateral add to 360°.
- An equilateral triangle has three equal sides and three 60° angles. An isosceles triangle has two equal sides and two equal base angles.
- In a circle, the diameter is twice the radius. Circumference = π × diameter; area = π × radius².
- A rectangle has area length × width; a triangle has area ½ × base × height.
- A line of symmetry divides a shape into two matching halves.
Worked example
A triangle has angles of 65° and 48°. Find the third angle. The three angles must add to 180°. First add the known angles: 65 + 48 = 113. Then subtract from 180: 180 − 113 = 67. The third angle is 67°, which is acute.
Traps that cost marks
Do not use 360° for a triangle or 180° for a quadrilateral. Do not call the radius the diameter. Keep the same unit throughout an area calculation. A diagram may not be drawn to scale, so use the given numbers, not the look of the shape. For a triangle's area, use the perpendicular height, not a sloping side.