if two non parallel side of trapezium are equal that it is cycle
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Step-by-step explanation:if two non parallel sides are equal in trapezium then it is called as isosceles trapezium
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prove that if non parallel sides of a trapezium are equal than prove that it is cyclic
Asked by Ravinder
Mar 8
person
2 Answers
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Syeda , SubjectMatterExpert
Member since Jan 25 2017
Answer.
In ΔAED and ΔBFC,
AD = BC (Given)
DE = CF (Distance between parallel sides is same)
∠AED = ∠BFC = 90°
ΔAED ≅ ΔBFC (RHS Congruence criterion)
Hence ∠DAE = ∠CBF (CPCT) … (1)
Since AB||CD, AD is transversal
∠DAE + ∠ADC = 180° (Sum of adjacent interior angles is supplementary)
⇒ ∠CBF + ∠ADC = 180° [from (1)]
Since sum of opposite angles is supplementary in trapezium ABCD.
Thus ABCD is a cyclic trapezium
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person
Kishore , Student
Member since Dec 10 2008
In ΔAED and ΔBFC,
AD = BC (Given)
DE = CF (Distance between parallel sides is same)
∠AED = ∠BFC = 90°
ΔAED ≅ ΔBFC (RHS Congruence criterion)
Hence ∠DAE = ∠CBF (CPCT) … (1)
Since AB||CD, AD is transversal
∠DAE + ∠ADC = 180° (Sum of adjacent interior angles is supplementary)
⇒ ∠CBF + ∠ADC = 180° [from (1)]
Since sum of opposite angles is supplementary in trapezium ABCD.
Thus ABCD is a cyclic trapezium
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