Question

In the given figure, AE = DE and BC || AD. Prove that the points A,B,C and D are concyclic. Also, prove that the diagonals of the quadrilateral ABCD are equal.

Answer 1

AE=DE
`angleA=angleD`
BC||AD
`angleECB=angleA`
`angleECB=angleEBC`
EB=EC
`angleB+angleD=180^o`
`angleA+angleC=180^o`
so, this is a concyclic Quadrilateral
In `/_ABC and /_BCD`
BC=BC(same)
AB=CD(given)
`angleABC=angleBCD`
`/_ABCcong/_BCD (SAS)`
so, we can say that AC=BD.