Question

show that cyclic trapezium is isosceles​

Answer 1

Answer:

Step-by-step explanation: let ABCD be the cyclic trapezium with

AB IICD.

thus' C draw CE parallel to AD meeting AB in E.

So,

AECD is a parallelogram.

so,

angle D=angle AEC.... opp angles of a parallelogram are equal....(i)

but,

angle D+angle ABC=180... opp angles of a cyclic quadr are supplementary....(ii)

from (i) and (ii)

angle AEC+angle ABC=180

but,

angle AEC+angle CEB= 180...linear pair

so,

angle ABC= angle CEB ..(iii)

so,

CE=CB... sides opp equal angles are equal.(iv)

but,

CE=AD...opp sides of parallelogram AECD.

from (iv)

we get,

AD=CB

Thus cyclic quadri ABCD is isoceles.

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Answer 2

let ABCD be the cyclic trapezium with

AB IICD.

thus' C draw CE parallel to AD meeting AB in E.

So,

AECD is a parallelogram.

so,

angle D=angle AEC.... opp angles of a parallelogram are equal....(i)

but,

angle D+angle ABC=180... opp angles of a cyclic quadr are supplementary....(ii)

from (i) and (ii)

angle AEC+angle ABC=180

but,

angle AEC+angle CEB= 180...linear pair

so,

angle ABC= angle CEB ..(iii)

so,

CE=CB... sides opp equal angles are equal.(iv)

but,

CE=AD...opp sides of parallelogram AECD.

from (iv)

we get,

AD=CB

Thus the cyclic trapezium ABCD is isoceles.

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