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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

In Fig. 16.195, <RD Sharma - Mathematics

<span lang="EN-USRS Aggarwal & V Aggarwal - Mathematics

<span lang="EN-USRS Aggarwal & V Aggarwal - Mathematics

PQRS is a RD Sharma - Mathematics

ABCD is a RD Sharma - Mathematics

<span lang="EN-USRS Aggarwal & V Aggarwal - Mathematics

<span lang="EN-USRS Aggarwal & V Aggarwal - Mathematics

<span lang="EN-USRS Aggarwal & V Aggarwal - Mathematics

<span lang="EN-USRS Aggarwal & V Aggarwal - Mathematics

ABCD is a RD Sharma - Mathematics