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NSC / Matric Euclidean geometry — practice questions

Explore 2 free Euclidean geometry questions in NSC / Matric 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 1–2 of 2.

The midpoints of two sides of a triangle are joined by a straight line. What is true of that line?Read the answer and worked solution →Two triangles stand on the same base and lie between the same pair of parallel lines. What follows?Read the answer and worked solution →

Worked practice questions

The midpoints of two sides of a triangle are joined by a straight line. What is true of that line?

  1. Parallel to the third side
  2. Equal to the third side
  3. At right angles to one side
  4. Twice as long as one side
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Correct answer: A. Parallel to the third side

1. The two chosen points sit exactly halfway along their sides. 2. The line joining them runs parallel to the remaining side of the triangle. 3. It is also exactly half as long as that remaining side. 4. Those two facts together make up the mid-point theorem. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 8: Euclidean geometry_

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Two triangles stand on the same base and lie between the same pair of parallel lines. What follows?

  1. They are congruent shapes
  2. They are right angled
  3. They are equal in area
  4. They are similar shapes
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Correct answer: C. They are equal in area

1. The area of a triangle depends on its base and its perpendicular height. 2. Two parallel lines stay the same distance apart everywhere between them. 3. So both triangles have the same height as well as the same base. 4. Equal base and equal height give equal area, however different the shapes look. 5. Congruence would need matching sides and angles, which does not follow here. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 8: Euclidean geometry_

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