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

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

Consider a trapezium with || and
Draw AM perpendicular to CD and BN perpendicular to CD.
In triangle and triangle ,
..................................................... (Given)
< = < ........................................ (By construction, each is �)
.................................................... (Perpendicular distance between two parallel lines is same)
Δ congruent Δ............................................... (RHS congruence rule)
< = < ................................................. (CPCT) ... (1)
< and < .............................................. are on the same side of transversal AD.
< + < = � ...................................... (2)
< + < = �.................................... [Using equation (1)]
This equation shows that the opposite angles are supplementary.
Therefore, is a .

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