Congruence in a bow-tie figure

Congruence in a bow-tie figure

Secondary 2
TGM Original Questions

Segments \(AD\) and \(BC\) intersect at \(F\). It is given that \(BF=CF\) and \(\angle ABF=\angle DCF\).

  1. Name the congruent triangles in the correct order and state the criterion.
  2. Given \(AD=15\) cm and \(AB=11\) cm:
    1. find \(AF\)
    2. explain why \(\triangle BFC\) is isosceles
    3. find \(DC\).

Solution:

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Answer:(a) \(\triangle ABF\cong\triangle DCF\), ASA; (b)(i) \(7.5\) cm; (ii) \(BF=CF\); (iii) \(11\) cm.

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