Isosceles trapezoid by definition has its non-parallel sides and base angles equal. Consider an isosceles trapezoid ABCD with base angles <ADC =  <BCD, non-parallel sides AD = BC and AB//CD

A cyclic quadrilateral has opposite angles supplementary i.e. <ADC + <ABC = 180 and <DAB + <BCD=180

Since AB//CD and AD & DC are transverse lines

<DAB + <ADC=180 and <ABC + <BCD = 180

Since <ADC = <BCD

<DAB + <ADC = <DAB + <BCD =180

Similarly, <ADC + <ABC = 180

so an isosceles trapezoid is a cyclic quadrilateral.

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