PQRS is a trapezium with PQ || SR and PS=QR. Prove that that trapezium is cyclic.
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Okay so draw altitudes pm and qn
Now prove triangles pms and qnr congruent by rhs congruency.
So now by cpct angle psm = angle qrn
Now since pq and Sr are parallel
Angle psm + angle spq = 180°
But angle psm = angle qrn
Therefore angle qrn + angle spq = 180°
Hence proved
Now prove triangles pms and qnr congruent by rhs congruency.
So now by cpct angle psm = angle qrn
Now since pq and Sr are parallel
Angle psm + angle spq = 180°
But angle psm = angle qrn
Therefore angle qrn + angle spq = 180°
Hence proved
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