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
Expert Answer
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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