Question

PLEASE SOLVE AND SEND ME THE SOLUTION

Answer 1

Step-by-step explanation:

Question

AE is the bisector of ∠CAD. Also , BA∥CE and AB=AC. Prove that

(i) ∠EAC=∠ACB and

(ii) ABCE is a parallelogram.

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Answer

ABCE is a parallelogram

AB=AC⇒∠ABC=∠ACB

Let ∠ ABC = ∠ ACB = x

∠BAC=180°−2x [Angle sum property]

AB∥CE⇒∠BAC=∠ACE

∠BAC=∠ACE=(180°−2x)

∠BAC+∠EAC+∠EAD=180° [Linear Pair]

(180°−2x)+2∠EAC=180°

2∠EAC=2x

∠EAC=x

Therefore, ∠EAC=∠ACB

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∠EAC=∠ACB⇒AE∥BC

Therefore, ABCE is a parallelogram.