Ask a Teacher

Search



Show that any four vertices of a regular pentagon form a cyclic quadilateral.

Let ABCDE a regular pentagon.
It is required to show ABCD is a cyclic quadrilateral.

In ?AED, AE = ED (Sides of regular pentagon ABCDE)
? ?EAD = ?EDA
In ?AED, ?AED + ?EAD + ?EDA = 180
? 108 + ?EAD + ?EAD = 180
? 2?EAD = 180– 108 = 72
? ?EAD = 36
? ?EDA = 36
?BAD = ?BAE – ?EAD = 108 – 36 = 72
In quadrilateral ABCD, ?BAD + ?BCD = 108 + 72 = 180
?ABCD is a cyclic quadrilateral


comments powered by Disqus