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O-Level Congruence alongside similarity
What the O-Level syllabus expects for Congruence alongside similarity, and how to practise it.
What the syllabus expects
- shapes that are congruent as well as shapes that are similar
- what characterises similar polygons and triangles, that is, corresponding angles being equal while corresponding sides stay in proportion
- scaling a plane figure up or down
- drawings made to scale
- how one constructs, and the defining features of, the perpendicular bisector of a line segment and the bisector of an angle
- judging whether a given pair of triangles is congruent or is similar
- how the areas of two similar plane figures compare as a ratio
- how the volumes of two similar solids compare as a ratio
- working through straightforward problems built on congruence and similarity
How it's examined
Questions on this topic most often ask you to find.
Worked examples
Example 1 (3 marks)
With triangle CED = 15 cm² and triangle AEB = 60 cm² in trapezium ABCD (AB = 12, DC = 6), find the area of the whole trapezium.
Show the worked answer
ABCD is a trapezium with AB parallel to DC, AB = 12 cm and DC = 6 cm, and E is the point where the diagonals cross. The height of the trapezium is the perpendicular distance between the parallel sides AB and DC, and E lies between them, so that height splits into the height of triangle AEB plus the height of triangle CED. Step 1 - height of triangle AEB, taking AB as its base. Area of a triangle = ½ × base × height, so ½ × 12 × h₁ = 60 6h₁ = 60 h₁ = 10 cm. Step 2 - height of triangle CED, taking DC as its base. ½ × 6 × h₂ = 15 3h₂ = 15 h₂ = 5 cm. Step 3 - height of the trapezium. The two heights are measured from E towards the two parallel sides, in opposite directions, so together they make up the full distance between AB and DC: height = h₁ + h₂ = 10 + 5 = 15 cm. Step 4 - area of the trapezium. Area = ½ × (sum of the parallel sides) × height = ½ × (12 + 6) × 15 = ½ × 18 × 15 = 9 × 15 = 135 cm².
More O-Level Elementary Maths (E-Maths) topics
Whole numbers and the operations performed on them · Ratio and proportion · Percentage · Rate and speed · Algebraic expressions and formulae · Functions together with their graphs · all of O-Level Elementary Maths (E-Maths)