SOLUTION: If two non parallel sides of a trapezium are equal, prove that it is cyclic.

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Question 934674: If two non parallel sides of a trapezium are equal, prove that it is cyclic.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If AD+=+CB then the trapezoid ABCD is a cyclic-quadrilateral.

Consider a trapezium ABCD with AB ||CD and AD=BC
Draw AM perpendicular to CD and BN perpendicular to CD.
In triangle AMD and triangle BNC,
AD+=+BC..................................................... (Given)
< AMD = < BNC........................................ (By construction, each is 90°)
AM+=+BM.................................................... (Perpendicular distance between two parallel lines is same)
Δ AMD congruent ΔBNC............................................... (RHS congruence rule)
< ADC = < BCD................................................. (CPCT) ... (1)
< BAD and < ADC.............................................. are on the same side of transversal AD.
< BAD + <+ADC = 180° ...................................... (2)
< BAD + < BCD = 180°.................................... [Using equation (1)]
This equation shows that the opposite angles are supplementary.
Therefore, ABCD is a cyclic+quadrilateral.