# Q : 6     ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if              necessary) at E. Prove that .

Given: ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E.

To prove :   AE = AD

Proof :

ADC = 3  , ABC = 4, ADE = 1  and AED = 2

.................1(linear pair)

....................2(sum of opposite angles of cyclic quadrilateral)

3 = 4      (oppsoite angles of parallelogram )

From 1 and 2,

3+1 = 2 +

From 3,    1 =

From 4,    AQB,     1 = 2

Therefore, AE = AD (In an isosceles triangle ,angles oppsoite to equal sides are equal)

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