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Chapter 10 Practice Paper: Congruence and Similarity — question paper

QuizQuipPractice Series
QQ/S3EM/CH10

Secondary 3 · Elementary Mathematics (G2 / G3)

Chapter 10 Practice Paper

Congruence and Similarity

Duration: 40 minutes
Total: 30 marks
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Class:
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Date:

READ THESE INSTRUCTIONS FIRST

  • Write your name, class and register number in the spaces at the top of this page.
  • Answer all questions.
  • Show all necessary working. Omission of essential working will result in loss of marks.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
  • Geometrical instruments and an approved calculator may be used.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 10 (G2 Congruence and Similarity: congruence tests, similar triangles, scale drawings, area and volume ratios).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures where appropriate.

  1. 1

    This question tests the congruence conditions.

    1. (a)

      Two triangles have all three pairs of sides equal. Name the congruence test.

      [1]
    2. (b)

      State the congruence test for two right-angled triangles whose hypotenuses, and one other pair of sides, are equal in turn.

      [1]
    3. (c)

      Explain why two triangles with all three angles equal need not be congruent.

      [1]
  2. 2

    Triangles ABC and PQR are similar with sides AB = 3 cm, BC = 4 cm, CA = 5 cm and PQ = 9 cm, QR = 12 cm, RP = 15 cm.

    1. (a)

      State the scale factor from ΔABC to ΔPQR.

      [1]
    2. (b)

      Write down the ratio of their perimeters.

      [1]
    3. (c)

      Find the ratio of their areas.

      [2]
  3. 3

    A vertical stick of height 1.5 m casts a shadow 2 m long. At the same moment, a tower casts a shadow 40 m long.

    1. (a)

      Explain why the two triangles formed are similar.

      [2]
    2. (b)

      Find the height of the tower.

      [2]
  4. 4

    A house plan is drawn to a scale of 1 : 100.

    1. (a)

      A wall measures 7 cm on the plan. Find its real length.

      [2]
    2. (b)

      A room has a real floor area of 12 m². Find its area on the plan.

      [2]
  5. 5

    Triangles PQR and XYZ are similar. PQ = 5 cm corresponds to XY = 7.5 cm, and QR = (2x + 1) cm corresponds to YZ = 18 cm.

    1. (a)

      Find the scale factor from ΔPQR to ΔXYZ.

      [2]
    2. (b)

      Find x.

      [2]
    3. (c)

      The perimeter of ΔPQR is 24 cm. Find the perimeter of ΔXYZ.

      [1]
  6. 6

    Two similar water containers have volumes 128 cm³ and 250 cm³.

    1. (a)

      Find the ratio of their heights, in simplest form.

      [3]
    2. (b)

      Find the ratio of their total surface areas.

      [2]
  7. 7

    A model car is built to a scale of 1 : 20 (model : real).

    1. (a)

      The model is 12 cm long. Find the real length in metres.

      [2]
    2. (b)

      The real car is 1.6 m wide. Find the width of the model.

      [1]
    3. (c)

      The model’s surface area is 250 cm². Find the real surface area in square metres.

      [2]

— End of paper —