Question

Prove that a cyclic trapezium is isosceles​

Answer 1

☞QUESTION:Prove that a cyclic trapezium is isosceles

✎Let ABCD be a cyclic trapezium, with AB || DC and AB is shorter than CD.

➽There are 4 angles in a trapezium and the trapezium is cyclic the opposite angles must be supplementary. Thus <A + <C = 180 deg. and <B + <D = 180 deg.

➽If AB and CD are parallel to each other, <A + <D = 180 deg. and <B + <C = 180 deg.

➽So <A + <C = 180 = <A + <D or <C = <D and acute.

➽Similarly, <B + <D = 180 = <A + <D or <A = <B and obtuse.

➽Thus the adjacent angle on parallel sides are equal. Therefore the trapezium is isosceles as well as cyclic

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Answer 2

Answer:

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