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pqrs is a trapezium with PQ …

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pqrs is a trapezium with PQ parallel to SR and PS equal to QR prove that the trapezium is cyclic
  • 2 answers

Gaurav Rana 4 years, 11 months ago

Construction =draw pn perpendicular sr and qm perpendicular sr Proof =In triangle psn and triangle qmr PS =QR (given) Angle PNS =Angle QMR ( each 90°) PN= QM(perpendicular distance between two ll lines always equal) Triangle PSN =~(means congurent to) triangle QMR ( by RHS ) Angle SPN =Angle RQM(by CPCT) Adding 90° both sides Angle P= Angle Q Angle S +Angle P=180°( by co- interior) Angle S+Angle Q=180°( angle P = Angle Q) Angle R +Angle Q =180°(by co -interior ) Angle R+Angle P =180°(Angle P=Angle Q) Since sum of the opposite angle of the trapezium is 180° hence it is a cyclic trapezium

Gaurav Rana 4 years, 11 months ago

Given=PQRS is a trapezium in which PS =QR and PQ ||SR To prove = angle p+ angle R = 180°and angle S + angle Q=180°
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