Question

ABCD is a quadrilateral in which all four sides are equal. Show that both pairs of opposite sides are parallel.​

Answer 1

ABCD is a quadrilateral in which ,

AB=BC=CD=DA

To Prove :- AB||CD and BC ||DA

construction :- join A to C

Proof:- In triangle ABC and triangle ADC

AB=DC (given)

BC=AD (given)

AC=AC (common in both triangles)

so, trianlge ABC congruence triangle ADC (by side angle side criteria)

AB||CD [anlge BAC = angle DAC ( alternat interior angle)]

BC||AD [angleBCA =angle DAC (alternat interior angle)]

Proved.