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Answer:
Given:
In Rhombus QRST, diagonals QS and RT intersect at W and U∈QR and point V∈RT such that UV⊥QR. (shown in below diagram)
To prove: QW•UR =WT•UV
Proof:
In a rhombus diagonals bisect perpendicularly,
Thus, in QRST
QW≅WS, WR ≅ WT and m∠QWR=m∠QWT=m∠RWS=m∠TWS=90°.
In triangles QWR and UVR,
(Right angles)
(Common angles)
By AA similarity postulate,
The corresponding sides in similar triangles are in same proportion,
(∵ WR ≅ WT )
Hence, proved.
