The diagonals of the cyclic quadrilateral ABCD are congruent.
So show, AD = BC and line AB || Line DC
Answers
Step-by-step explanation:
Line AB is parallel to line CD.
AD = BC
Step-by-step explanation:
First, we draw a cyclic quadrilateral and draw the diagonals. They intersect at the point O. (refer the figure attached)
It is given that both the diagonals are congruent.
It means that the lengths of both diagonals are equal.
Therefore, length of OA = length of OC
And, length of OB = length of OD
Since, Both the diagonals are equal in length.
So, we can write as;
length of OA = length of OC = length of OB = length of OD
Hence, we can say that \Delta OAB, \Delta OBC, \Delta OCD, \Delta ODAΔOAB,ΔOBC,ΔOCD,ΔODA are isosceles triangles.
Also, \angle AOB = \angle BOC = \angle COD = \angle DOA = \dfrac {360^o}{4} = 90^o∠AOB=∠BOC=∠COD=∠DOA=
4
360
o
=90
o
Thus, we can conclude that the lines of quadrilateral are equal in measures.
So, this quadrilateral is a square. It means, AD = BC.
Therefore, line AB is parallel to line CD.
please mark me as brainlist
