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Assume E is the intersection point of AB and DS.
Step-by-step explanation:
AB // CD, hence angle AED = angle EDC
=> angle AED = angle ABR ( = 1/2 of angle ABC)
=> DP // BR
The same for AR and CP, so we have AR//CP
Hence, RQRS is a parallelogram (1)
Besides, angle SAD = 1/2 of angle DAB
angle SDA = 1/2 of angle CDA
So, angle SAD + angle SDA = 1/2 (angle DAB + angle CDA) = 90 degree
So, angle DSA = 90 degree (2)
From (1) and (2) => PQRS is a rectangle
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