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Abcd is parallelogram in which p …

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Abcd is parallelogram in which p and q are mid points of opposw sides ab and CD. If aq intersects DP at s and bq intersects CP at r show that dpbq is parallelogram and psqr is parallelogram

Posted by Rajendra G M 8 years, 9 months ago

CBSE > Class 09 > Mathematics

1 answers

Neeraj Sharma 8 years, 9 months ago

{tex}ABCD\,is\,a\,||gm{/tex}

{tex}AB = DC{/tex}

{tex}{1 \over 2}AB = {1 \over 2}DC{/tex}

{tex}Since\,P\,and\,Q\,are\,the\,mid\,po{\mathop{\rm int}} s\,of\,AB\,and\,CD{/tex}

{tex}PB = DQ{/tex}

{tex}also\,PB||DQ{/tex}

{tex}Hence\,DPBQ\,is\,a\,||gm{/tex}

{tex} \Rightarrow DP||BQ \ldots \ldots \left( 1 \right){/tex}

{tex}similarly{/tex}

{tex}APCQ\,is\,a\,||gm{/tex}

{tex} \Rightarrow AQ||BC \ldots \ldots \left( 2 \right){/tex}

{tex}From\,\left( 1 \right)\,and\,\left( 2 \right){/tex}

{tex}DP||BQ\,and\,AQ||BC{/tex}

{tex} \Rightarrow SP||QR\,and\,SQ||PR{/tex}

{tex}Hence\,PSQR\,is\,a\,||gm{/tex}

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CBSE > Class 09 > Mathematics