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Question

In the given figure B and E are points on the line segment AC and DF respectively. Show that AD || CF.


Solution


ABED and BCFE are cyclic quadrilaterals
CBE is external angle to ABED
CBE=ADE
But CBE+CFB=180
ADE+CEB=180
Similarity
BAD+BCF=180
AC is transversal between AD and CF
and BAD and BCF are internal angles and their sum is 180
+ADE and CFE are internal angles and their sum is 180
AD is parallel to CF.
 

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