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Congruence in a bow-tie figure

Congruence in a bow-tie figure

Secondary 2
8 marks
TGM Original Questions

Optional extension

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]
  2. Given \(AD=15\) cm and \(AB=11\) cm:
    1. find \(AF\)[2]
    2. explain why \(F\) is the midpoint of \(BC\)[2]
    3. find \(DC\).[2]

Solution:

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Answer:(a) \(\triangle ABF\equiv\triangle DCF\), ASA (b)(i) \(7.5\text{ cm}\) (ii) \(B,F,C\) are collinear and \(BF=CF\) (iii) \(11\text{ cm}\)

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