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Congruence and similarity in a compound figure

Congruence and similarity in a compound figure

Secondary 2
8 marks
TGM Original Questions

Optional extension

In the diagram, \(AB=AQ\), \(PA=QS\), and \(AB\parallel QR\). Lines \(QR\) and \(AC\) are produced to meet at \(S\).

  1. Name the triangle congruent to \(PAB\).[2]
  2. Show that \(\triangle PAC\sim\triangle SRC\).[2]
  3. Given \(AP=16\) cm, \(AC=4\) cm and \(RS=11\) cm, find
    1. \(CR\),[2]
    2. \(AB\).[2]

Solution:

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Answer:(a) \(\triangle SQA\) (b) AA proof (c)(i) \(\dfrac{11}{4}\text{ cm}\) (ii) \(4\text{ cm}\)

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