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ECZ Grade 12 School Certificate Euclidean geometry — practice questions

Explore 6 free Euclidean geometry questions in ECZ Grade 12 School Certificate Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Euclidean geometry questions and exercises with answers

Showing questions 1–6 of 6.

What is an established or accepted principle called?Read the answer and worked solution →A line from the centre of a circle is drawn perpendicular to a chord. What does it do?Read the answer and worked solution →What is true of the opposite angles of a cyclic quadrilateral?Read the answer and worked solution →An arc subtends an angle of 80 degrees at the centre of a circle. What angle does it subtend at the circumference?Read the answer and worked solution →A chord of length 16 units lies in a circle of radius 10 units. How far is the chord from the centre?Read the answer and worked solution →Fill the circle geometry boardRead the answer and worked solution →

Worked practice questions

What is an established or accepted principle called?

  1. A theorem
  2. A converse
  3. An axiom
  4. A chord
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Correct answer: C. An axiom

1. Some statements in geometry are accepted without any proof. 2. An axiom is an established or accepted principle. 3. A theorem is different, because it has to be shown to be true by argument. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 8: Euclidean geometry_

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A line from the centre of a circle is drawn perpendicular to a chord. What does it do?

  1. It bisects the chord
  2. It extends the chord
  3. It doubles the chord
  4. It shortens the chord
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Correct answer: A. It bisects the chord

1. A chord is a straight line joining the ends of an arc. 2. A line drawn from the centre perpendicular to that chord bisects it. 3. So the chord is cut into two pieces of equal length. 4. The reverse also holds, since a line from the centre to the mid-point of a chord is perpendicular to it. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 8: Euclidean geometry_

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What is true of the opposite angles of a cyclic quadrilateral?

  1. They are equal in size
  2. They are supplementary
  3. They are both acute
  4. They are right angles
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Correct answer: B. They are supplementary

1. A cyclic quadrilateral has all four of its vertices on the circumference of a circle. 2. Its opposite angles are supplementary, so each pair adds up to a straight angle. 3. The reverse is also true, since supplementary interior opposite angles make a quadrilateral cyclic. 4. Opposite angles being equal belongs to a parallelogram, which need not be cyclic at all. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 8: Euclidean geometry_

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