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# CBSE Class 9 Answered

if ABCD is a llgm and X and Y are points on the diagonal BD such that DX=BY. Prove that a) AXCY is a llgm
Asked by borakartike2 | 29 Dec, 2023, 09:21: PM

Let ABCD be given parallelogram . X and Y are points on diagonal BD so that BX = DY .

Let us consider ΔAYD and ΔBXC .

ADY = CBX  ( alternate angles because AD || BC )

AD = BC ( opposite sides of parallelogram )

DY = BX ( given )

Hence by SAS criteria , ΔAYD ΔBXC  and  AY = CX

Similarly , we prove ΔAXB and ΔCYD are congruent and AX = CY

Since opposite sides are equal, quadrilateral AXCY is parallelogram .

Answered by Thiyagarajan K | 29 Dec, 2023, 11:19: PM

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