1. In Parallelogram
ABCD, opposite angles are always equal.
2. In a cyclic quadrilateral, the sum of a pair of opposite angles is
180∘3. The sum of angles of a linear pair is always equal to
180∘.
4. The angles opposite to the equal sides are equal in measure.
∠ABC=∠ADC=θ‌‌( Theorem 1
)∠ABC+∠AED=180∘‌‌( Theorem 2
)⇒∠AED=180∘−θ∠ADE+θ=180∘‌‌( Theorem 3)
⇒∠ADE=180∘−θFrom equation (1) \& (2)
∠AED=∠ADEStatement: 1
We know that,
∠AED=∠ADEFrom theorem 4,
AE=ADHence, statement 1 is correct.
Statement: 2
CD=DE is only possible if
D become the centre of the circle and
CD, DE radius. but we take
D from the centre, parallelogram
ABCD will not be possible such that
A,B&C lies on the circle and
AB=CD&‌BC=ADHence, statement 2 is incorrect.