Geometry

Traps in Geometry

• Applies the rule for a different situation
  Identify the situation first (angle at centre? opposite angles of a cyclic quadrilateral? reverse bearing?) and write the rule that belongs to it before calculating.
• Calculates a different quantity
  Name the quantity and its unit before you start (remainder; horizontal distance; cm²). After calculating, check your number is that quantity and not a neighbour.
• Wrong angle-sum fact
  Triangle: 180°. Quadrilateral: 360°. n-sided polygon: (n − 2) × 180° for interior angles; exterior angles always total 360°.
• Treats one part of a ratio as the total
  In a : b, total parts = a + b. One part = amount ÷ (a + b). Then multiply by the part you need.
• Stops one step short of the answer
  Before writing the answer, re-read the question's last words (each angle? neither? Ama's share? variance?). Ask: is my number that thing, or a stage on the way to it?
• Repeats a given value as the answer
  If your answer equals a number in the question, check whether the rule really leaves it unchanged. Most rules transform the given value.
• Uses the wrong operation
  Write the rule in words first (bearing back = bearing ± 180°; IQR = Q₃ − Q₁), then substitute. Estimate: does the size of the answer make sense?
• Careless calculation
  Not a knowledge gap — a checking gap. Re-read the question, estimate the answer first, and check every line before you choose an option.
• Sign slip when moving or multiplying terms
  Moving a term across "=" means doing the opposite operation to BOTH sides. And (−)×(−) = (+). Write each step on a new line; circle every minus sign before you expand.
• Incomplete inverse operations
  Undo operations in REVERSE order, one at a time, to the whole of each side. Make a list: what was done to x? Undo the last one first. Check by substituting back.
• Inverts a relationship
  Say the rule with its direction (angle at centre = TWICE the angle at the circumference; (x − 1) = 0 gives x = +1). Check your answer against a simple case.
• Uses 360° where 180° applies
  Angles on a straight line and opposite angles of a cyclic quadrilateral add to 180°; angles at a point add to 360°. Sketch the figure to see which one you have.
• Mixes up circle theorems
  Centre angle = 2 × circumference angle (same arc); angles in the same segment are equal; opposite angles of a cyclic quadrilateral add to 180°.