2026 NCHS P1 Q17

2026 NCHS P1 Q17

Secondary 4
3 marks

In the diagram, \(ABC\) is a triangle. \(D\) is a point on \(AC\) such that \(AB=BD\) and \(ACE\) is a straight line. Angle \(ABD=(2x)^\circ\) and angle \(BCE=(135-\frac12x)^\circ\).

Prove that triangle \(ABC\) is an isosceles triangle.[3]

Solution:

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Answer:\(\angle ABC=\angle ACB=(45+\frac12x)^\circ\), hence \(AB=AC\).

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