Midpoint and parallel-line area reasoning

Midpoint and parallel-line area reasoning

Secondary 2
TGM Original Questions

In \(\triangle ABC\), \(D\) lies on \(AB\), \(AD=3\) cm, \(DB=6\) cm, \(BC=12\) cm, and \(E\) is the midpoint of \(BC\). The line through \(D,E\) is parallel to \(AF\), where \(F\) lies on \(BC\).

  1. Name a triangle similar to \(BED\).
  2. Find \(BF\).
  3. Find \(EF:FC\).
  4. The perpendicular distance from \(D\) to \(BE\) is \(4\) cm. Find the area of \(\triangle ABF\).

Solution:

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Answer:(a) \(\triangle BAF\); (b) \(9\) cm; (c) \(1:1\); (d) \(27\text{ cm}^2\).

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