NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Congruence and similarity algorithms

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A walking route in Sydney is designed using two triangular sections, Triangle ABC and Triangle DEF. Triangle ABC has side lengths AB = 24 m, BC = 34 m, and AC = 34 m.

Triangle DEF has side lengths DE = 24 m, EF = 34 m, and DF = 34 m. An algorithm is used to determine if the triangles are congruent by checking if all corresponding sides are equal in length and in the same order.

Using the SSS (side-side-side) congruence criterion, what is the exact result of the algorithm's comparison? Answer exactly as 'congruent' or 'not congruent'.

Triangle ABC side measurementsAB = 24 m; AC = 34 m; BC = 34 mABC24 m34 m34 m
Measurements from the question · not to scale.
Triangle DEF side measurementsDE = 24 m; DF = 34 m; EF = 34 mDEF24 m34 m34 m
Measurements from the question · not to scale.
Concept illustrations

These are separate worked examples of related concepts, not a diagram of this question. Their values and dimensions do not describe your question.

Classifying from known properties. For a quadrilateral already known to have four right angles, check whether all four sides are equal. Yes gives a square; no gives a rectangle that is not a square. A square remains a rectangle too.4 right anglesRectangle→4 equal sides?Check lengths→Yes: squareNo: non-square
For a quadrilateral already known to have four right angles, check whether all four sides are equal. Yes gives a square; no gives a rectangle that is not a square. A square remains a rectangle too.
Squares belong to two broader families. A square is both a rectangle and a rhombus. The arrows mean “is a type of”, not a step in a calculation.RectangleRhombusSquare
A square is both a rectangle and a rhombus. The arrows mean “is a type of”, not a step in a calculation.

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Worked solution

  1. Given: Triangle ABC has side lengths AB = 24 m, BC = 34 m, AC = 34 m.
  2. Given: Triangle DEF has side lengths DE = 24 m, EF = 34 m, DF = 34 m.
  3. To determine congruency using SSS criterion, all three corresponding sides must be equal in length and in the same order.
  4. Match corresponding sides: AB corresponds to DE, BC to EF, and AC to DF.
  5. Compare AB and DE: 24 m = 24 m → equal.
  6. Compare BC and EF: 34 m = 34 m → equal.
  7. Compare AC and DF: 34 m = 34 m → equal.
  8. All three pairs of corresponding sides are equal in length and in the same order.
  9. By the SSS (side-side-side) congruence criterion, if all three corresponding sides of two triangles are equal, the triangles are congruent.
  10. Therefore, the algorithm correctly identifies the triangles as congruent.
  11. The result of the algorithm's comparison is 'congruent'.
  12. Final verification: all side lengths match exactly, and the order of comparison follows the SSS rule.

Reference answer: congruent

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