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Geometrical Constructions

7 Grade 7 Mathematics questions on Geometrical Constructions, with worked marking schemes. 7 questions are available on this topic in full.

  1. Question 1

    1 mark

    A perpendicular bisector of a line segment divides it into:

    A. Two equal halves at 90°

    B. Two equal halves at 45°

    C. Four parts

    D. Two unequal parts

    (1 mark)

    Marking scheme

    A. Two equal halves at — the word does both jobs: 'bisector' means it cuts the segment into two equal parts, and 'perpendicular' means it crosses at a right angle. B keeps the halving but gets the angle wrong.

  2. Question 2

    3 marks

    Construct the perpendicular bisector of a line segment AB = 8 cm. Describe the steps.

    (3 marks)

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  3. Question 3

    4 marks

    Construct triangle PQR where PQ = 7 cm, angle P = 60° and angle Q = 50°. Measure PR.

    (4 marks)

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  4. Question 4

    1 mark

    To bisect an angle, you need:

    A. A set square only

    B. A ruler only

    C. A protractor only

    D. A pair of compasses and a ruler

    (1 mark)

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  5. Question 5

    1 mark

    The perpendicular from a point to a line gives the:

    A. Diagonal distance

    B. Longest distance

    C. Parallel distance

    D. Shortest distance

    (1 mark)

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  6. Question 6

    1 mark

    An angle bisector divides an angle into:

    A. A right angle

    B. Two unequal angles

    C. Three equal angles

    D. Two equal angles

    (1 mark)

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  7. Question 7

    3 marks

    Describe how to construct a 60° angle using a compass and ruler.

    (3 marks)

    Marking scheme

    1. Draw a base line and mark point A.

    2. With compass at A, draw an arc crossing the line at B.

    3. With same radius at B, draw an arc crossing the first arc at C.

    4. Draw line AC. Angle BAC = 60°.

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