Mathematics

Problem

1. ABCD is a quadrilateral in which

\mathrm{P}, \mathrm{Q}, \mathrm{R}

and S are mid-points of the sides

\mathrm{AB}, \mathrm{BC}, \mathrm{CD}

and DA (see Fig 8.20). AC is a diagonal. Show that : (i)

\mathrm{SR} \| \mathrm{AC}

and

\mathrm{SR}=\frac{1}{2} \mathrm{AC}

(ii)

\mathrm{PQ}=\mathrm{SR}

(iii) PQRS is a parallelogram. ![](https://storage.googleapis.com/diraq-contents/question-bank/question-images/6f7d3fe9f967/2025_10_04_57cf2c481bb015ddda14g-10.jpg) Fig. 8.20

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