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

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,

Since AB is parallel to CD,

Comparing the above two equations, it can be said that

This is a property of an isosceles trapezium.

Thus, AD=BC.

Hence, it has been proven that AD=BC.

  • 54
What are you looking for?