Q. 84.3( 302 Votes )

If the non-parall

Answer :

Consider a trapezium ABCD with

AB | |CD and


BC = AD


Draw AM perpendicular to CD and BN perpendicular to CD



In ΔAMD and ΔBNC,


AD = BC (Given)


∠AMD = ∠BNC (By construction, each is 90°)


AM = BN (Perpendicular distance between two parallel lines is same)


ΔAMD ΔBNC (RHS congruence rule)


∠ADM = ∠BCN (CPCT) 
⇒∠ADC = ∠BCD  (i)


BAD and ADC are on the same side of transversal AD


∠BAD + ∠ADC = 180° (ii)


∠BAD + ∠BCD = 180° [Using equation (i)]


This equation shows that the opposite angles are supplementary


Therefore, ABCD is a cyclic quadrilateral.

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