CBSE Class 9 Answered

1) In EAD,

EA = ED

Let ∠EAD = x

Thus, ∠EAD =∠EDA = x  [angles opposite to equal sides are equal]

∠BCD +∠DAB =180⁰

∠BCD + x = 180 [since ∠DAB =∠DAE = x]

∠BCD = 180 - x

Similarly,

∠ABC = 180 - x

∠DAB +∠ABC = x + 180 - x

∠DAB +∠ABC =180⁰  

Similarly, ∠BCD + ∠CDA = 180⁰

Since the adjacent interior angles are supplementary, therefore

2) Since ,

∠EBC =∠EAD = x [corresponding angles are equal]

Similarly ∠ECB =∠EDA = x

Now, in triangle EBC,

∠EBC =∠ECB = x

Thus, EB = EC     [sides opposite to equal angles are equal]