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Revision

Chapter 8: Euclidean geometry

8.1 Revision (EMBJ6)

Parallelogram (EMBJ7)

  • Discuss terminology.
  • Converses are not examinable.
  • Good practice for answering questions:
  • make a neat and accurate drawing
  • state triangle/figure being considered
  • give statement and appropriate reason
  • give a conclusion

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Summary of the properties of a parallelogram:

  • Both pairs of opposite sides are parallel.

  • Both pairs of opposite sides are equal in length.

  • Both pairs of opposite angles are equal.

  • Both diagonals bisect each other.

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The mid-point theorem (EMBJ8)

The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half the length of the third side.

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Given: \(AD = DB\) and \(AE = EC\), we can conclude that \(DE \parallel BC\) and \(DE = \frac{1}{2}BC\).