If two sides of a cyclic quadrilateral are parallel , prove tha the remaining two sides are equal and the - Maths - Circles

Question

If two sides of a cyclic quadrilateral are parallel , prove tha
the remaining two sides are equal and the diagonals are also
equal

Vimala · Accepted Answer

Consider the following figure:

ABCD is the cyclic quadrilateral It is given that AB is parallel to CD We need to prove that AD and BC are equal and that AC and BD are equal Since ABCD is a cyclic quadrilateral, $∠ D A B + ∠ D C B = ∠ C D A + ∠ C B A = 180^{\circ}$ Since AB is parallel to CD, $∠ D A B + ∠ C D A = ∠ D C B + ∠ C B A = 180^{\circ}$ Comparing the above two equations, it can be said that $∠ C D A = ∠ D C B$ This is a property of an isosceles trapezium Thus, AD=BC Hence, it has been proven that AD=BC

If two sides of a cyclic quadrilateral are parallel , prove tha the remaining two sides are equal and the diagonals are also equal