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GeometryQuestion and Answers: Page 25

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Given that ABCD is a trapezium such that AD//BC. The centroid of △ABD lies on the bisector of ∠BCD. Show that the centroid of △ABC lies on the bisector of ∠ADC.

$$\mathrm{Given}\:\mathrm{that}\:{ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{trapezium}\:\mathrm{such}\:\mathrm{that}\:{AD}//{BC}. \\ $$$$\mathrm{The}\:\mathrm{centroid}\:\mathrm{of}\:\bigtriangleup{ABD}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{bisector}\:\mathrm{of}\:\angle{BCD}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\bigtriangleup{ABC}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{bisector}\:\mathrm{of}\:\angle{ADC}. \\ $$

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