Nested parallel lines in a triangle

Nested parallel lines in a triangle

Secondary 2
TGM Original Questions

In \(\triangle ABC\), \(D\) lies on \(AB\), \(E\) on \(CB\), and \(F\) on \(AC\). Also \(FD\parallel CB\), \(FE\parallel AB\), and \(FE\) meets \(CD\) at \(G\).

  1. Name a triangle similar to \(GFD\).
  2. Name a triangle similar to \(DBC\).
  3. Given \(CE=6\) cm, \(EB=4\) cm and \(BD=6\) cm, find \(GF\).

Solution:

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Answer:(a) \(\triangle DBC\); (b) \(\triangle GFD\); (c) \(2.4\) cm.

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