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Anik Dutta Choudhury asked in Maths

Section C no 13

13.
  â€‹ABCD is a rectangle. X and Y are points on side AD and BC respectively such that AY = BX. Prove that AX = BY.

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Sanjari Kalantri answered this

Dear Student,

Given: ABCDis a rectangle, AY = BXTo prove: AX = BYProof: Since, ABCD is a rectangle, XAB = YBA = 90° - iIn AXB and BYA,AY = BX   GivenAB = AB   CommonXAB = YBA = 90°    From i By SAS congruence criterion,AXB  BYABy corresponding parts of congruent triangles (cpct),AX = BYHence, proved.