Question

if two non parallel sides of trapezium are equal then prove that it is cyclicquadrilateral​

Answer 1

Given:-

• A trapezium ABCD in which AB || CD and AD = BC.

To Prove :-

• ABCD is a cyclic quadrilateral.

Construction :-

• Draw AE and BF perpendicular on CD meeting CD at E and F respectively.

Proof :-

★ In ∆ AED and ∆ BFC

⟼AE = BF (Distance between parallel lines)

⟼AD = BC (Given)

⟼∠AED = ∠BFC (Each 90°)

⇛∆ AED ≅ ∆ BFC (RHS Congruency Rule)

∴ ∠ADE = ∠BCF (CPCT)

⇛∠ADC = ∠BCD

★Since, AB || CD

⇛ ∠BAD + ∠ADC = 180° ( Sum of cointeriors)

⇛ ∠BAD + ∠BCD = 180°

⇛ABCD is a cyclic quadrilateral.