2025 JVSS PRELIMS P2 Q2

2025 JVSS PRELIMS P2 Q2

Secondary 4
10 marks
2025 Jurongville Secondary School Prelims A Math Paper 2

\(ADE\) is a semicircle with centre \(O\). It is given that \(D\) and \(E\) are midpoints of \(AB\) and \(AC\) respectively and \(AB = BC\).

  1. Prove that \(\triangle ABE \cong \triangle CBE\).[3]
  2. Prove that \(\angle BEA = 90^\circ\).[1]
  3. Determine, with explanation, whether \(\triangle ADE\) is similar to \(\triangle ABC\).[3]
  4. Show that \(\dfrac{DF}{FC}=\dfrac{1}{2}\).[3]

Solution:

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Answer:(a) \(\triangle ABE\cong\triangle CBE\) (b) \(\angle BEA=90^\circ\) (c) \(\triangle ADE\sim\triangle ABC\) (d) \(\dfrac{DF}{FC}=\dfrac{1}{2}\)

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